In this paper the general notion of Bourbaki structures, interpreted in terms of Suppes predicates, will be used to axiomatize a system of meta-rankings in the sense introduced by A. K. Sen. It will be argued that this axiomatization must take place in a Kantian-ruled world in order to provide a link between meta-rankings and individual actions.Dedicated to Prof. Francisco A. Doria on his 50th birthday.

This paper calculates, in a precise way, the complexity of the index sets for three classes of computable structures: the class $K_{\omega _{1}^{\mathit{CK}}}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}$ , the class $K_{\omega _{1}^{\mathit{CK}}+1}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}+1$ , and the class K of all structures of non-computable Scott rank. We show that I(K) is m-complete $\Sigma _{1}^{1},\,I(K_{\omega _{1}^{\mathit{CK}}})$ is m-complete $\Pi _{2}^{0}$ relative to Kleen's O, and $I(K_{\omega _{1}^{\mathit{CK}}+1})$ is m-complete $\Sigma (...) _{2}^{0}$ relative to O. (shrink)

Rational consequence relations and Popper functions provide logics for reasoning under uncertainty, the former purely qualitative, the latter probabilistic. But few researchers seem to be aware of the close connection between these two logics. I’ll show that Popper functions are probabilistic versions of rational consequence relations. I’ll not assume that the reader is familiar with either logic. I present them, and explicate the relationship between them, from the ground up. I’ll also present alternative axiomatizations for each logic, showing them to (...) depend on weaker axioms than usually recognized. (shrink)

For countable structure, "Scott rank" provides a measure of internal, model-theoretic complexity. For a computable structure, the Scott rank is at most [Formula: see text]. There are familiar examples of computable structures of various computable ranks, and there is an old example of rank [Formula: see text]. In the present paper, we show that there is a computable structure of Scott rank [Formula: see text]. We give two different constructions. The first starts with an arithmetical example due to Makkai, (...) and codes it into a computable structure. The second re-works Makkai's construction, incorporating an idea of Sacks. (shrink)

The theory of ranked partial structures allows a reinterpretation of several of the standard results of model theory and first-order logic and is intended to provide a proof-theoretic method which allows for the intuitions of model theory. A version of the downward Löwenheim-Skolem theorem is central to our development. In this paper we will present the basic theory of ranked partial structures and their logic including an appropriate version of the completeness theorem.

We show that any structure of finite Morley Rank having the definable multiplicity property has a rank and multiplicity preserving interpretation in a strongly minimal set. In particular, every totally categorical theory admits such an interpretation. We also show that a slightly weaker version of the DMP is necessary for a structure of finite rank to have a strongly minimal expansion. We conclude by constructing an almost strongly minimal set which does not have the DMP in any rank preserving expansion, (...) and ask whether this structure is interpretable in a strongly minimal set. (shrink)

A superstable homogeneous structure is said to be simple if every complete type over any set A has a free extension over any B ⊇ A. In this paper we give a characterization for this property in terms of U-rank. As a corollary we get that if the structure has finite U-rank, then it is simple.

O-minimal structures have long been thought to occupy the base of a hierarchy of ordered structures, in analogy with the role that strongly minimal structures play with respect to stable theories. This is the first in an anticipated series of papers whose aim is the development of model theory for ordered structures of rank greater than one. A class of ordered structures to which a notion of finite rank can be assigned, the decomposable structures, (...) is introduced here. These include all ordered structures definable in o-minimal structures. The principal result in this paper, Theorem 5.1, asserts roughly that a decomposable structure [Formula: see text] can be partitioned into finitely many definable subsets such that on each set the restriction of < is a "twisted lexicographic" order. As a consequence, for all n and linear orders ≺ definable on a subset X ⊆ Mn in an o-minimal structure [Formula: see text], there is a definable partition of X such that the restriction of ≺ to each set in the partition is "lexicographic". (shrink)

For a supersimple SU-rank 1 theory T we introduce the notion of a generic elementary pair of models of T . We show that the theory T* of all generic T-pairs is complete and supersimple. In the strongly minimal case, T* coincides with the theory of infinite dimensional pairs, which was used in 1184–1194) to study the geometric properties of T. In our SU-rank 1 setting, we use T* for the same purpose. In particular, we obtain a characterization of linearity (...) for SU-rank 1 structures by giving several equivalent conditions on T*, find a “weak” version of local modularity which is equivalent to linearity, show that linearity coincides with 1-basedness, and use the generic pairs to “recover” projective geometries over division rings from non-trivial linear SU-rank 1 structures. (shrink)

Theorem: For every k, there is an expansion of the theory of algebraically closed fields (of any fixed characteristic) which is almost strongly minimal with Morley rank k.

We consider a universe of finite Morley rank and the following definable objects: a field math formula, a non-trivial action of a group math formula on a connected abelian group V, and a torus T of G such that math formula. We prove that every T-minimal subgroup of V has Morley rank math formula. Moreover V is a direct sum of math formula-minimal subgroups of the form math formula, where W is T-minimal and ζ is an element of G of (...) order 4 inverting T. (shrink)

We provide a general framework for studying the expansion of strongly minimal sets by adding additional relations in the style of Hrushovski. We introduce a notion of separation of quantifiers which is a condition on the class of expansions of finitely generated models for the expanded theory to have a countable ω-saturated model. We apply these results to construct for each sufficiently fast growing finite-to-one function μ from 'primitive extensions' to the natural numbers a theory T μ of an expansion (...) of an algebraically closed field which has Morley rank 2. Finally, we show that if μ is not finite-to-one the theory may not be ω-stable. (shrink)

Dual-ranking act-consequentialism (DRAC) is a rather peculiar version of act-consequentialism. Unlike more traditional forms of act-consequentialism, DRAC doesn’t take the deontic status of an action to be a function of some evaluative ranking of outcomes. Rather, it takes the deontic status of an action to be a function of some non-evaluative ranking that is in turn a function of two auxiliary rankings that are evaluative. I argue that DRAC is promising in that it can accommodate certain features of commonsense morality (...) that no single-ranking version of act-consequentialism can: supererogation, agent-centered options, and the self-other asymmetry. I also defend DRAC against three objections: (1) that its dual-ranking structure is ad hoc, (2) that it denies (putatively implausibly) that it is always permissible to make self-sacrifices that don’t make things worse for others, and (3) that it violates certain axioms of expected utility theory, viz., transitivity and independence. (shrink)

We say that a first order formula Φ distinguishes a structure M over a vocabulary L from another structure M' over the same vocabulary if Φ is true on M but false on M'. A formula Φ defines an L-structure M if Φ distinguishes M from any other non-isomorphic L-structure M'. A formula Φ identifies an n-element L-structure M if Φ distinguishes M from any other non-isomorphic n-element L-structure M'. We prove that every n-element structure M is identifiable by a (...) formula with quantifier rank less than (1- 1/2k)n+k²-k+4 and at most one quantifier alternation, where k is the maximum relation arity of M. Moreover, if the automorphism group of M contains no transposition of two elements, the same result holds for definability rather than identification. The Bernays-Schönfinkel class consists of prenex formulas in which the existential quantifiers all precede the universal quantifiers. We prove that every n-element structure M is identifiable by a formula in the Bernays-Schönfinkel class with less than (1-1/2k²+2)n+k quantifiers. If in this class of identifying formulas we restrict the number of universal quantifiers to k, then less than n-√ n+k²+k quantifiers suffice to identify M and, as long as we keep the number of universal quantifiers bounded by a constant, at total n-O(√ n) quantifiers are necessary. (shrink)

The first main result isolates some conditions which fail for the class of graphs and hold for the class of Abelian p-groups, the class of Abelian torsion groups, and the special class of "rank-homogeneous" trees. We consider these conditions as a possible definition of what it means for a class of structures to have "Ulm type". The result says that there can be no Turing computable embedding of a class not of Ulm type into one of Ulm type. We (...) apply this result to show that there is no Turing computable embedding of the class of graphs into the class of "rank-homogeneous" trees. The second main result says that there is a Turing computable embedding of the class of rank-homogeneous trees into the class of torsion-free Abelian groups. The third main result says that there is a "rank-preserving" Turing computable embedding of the class of rank-homogeneous trees into the class of Boolean algebras. Using this result, we show that there is a computable Boolean algebra of Scott rank ${\mathrm{\omega }}_{1}^{\mathrm{C}\mathrm{K}}$. (shrink)

Ranking theory is one of the salient formal representations of doxastic states. It differs from others in being able to represent belief in a proposition (= taking it to be true), to also represent degrees of belief (i.e. beliefs as more or less firm), and thus to generally account for the dynamics of these beliefs. It does so on the basis of fundamental and compelling rationality postulates and is hence one way of explicating the rational structure of doxastic states. Thereby (...) it provides foundations for accounts of defeasible or nonmonotonic reasoning. It has widespread applications in philosophy, it proves to be most useful in Artificial Intelligence, and it has started to find applications as a model of reasoning in psychology. (shrink)

With the wide adoption of social collaborative coding, more and more developers participate and collaborate on platforms such as GitHub through rich social and technical relationships, forming a large-scale complex technical system. Like the functionalities of critical nodes in other complex systems, influential developers and projects usually play an important role in driving this technical system to more optimized states with higher efficiency for software development, which makes it a meaningful research direction on identifying influential developers and projects in social (...) collaborative coding platforms. However, traditional ranking methods seldom take into account the continuous interactions and the driving forces of human dynamics. In this paper, we combine the bursty interactions and the bipartite network structure between developers and projects and propose the BurstBiRank model. Firstly, the burstiness between each pair of developers and projects is calculated. Secondly, a weighted developer-project bipartite network is constructed using the burstiness as weight. Finally, an iterative score diffusion process is applied to this bipartite network and a final ranking score is obtained at the stationary state. The real-world case study on GitHub demonstrates the effectiveness of our proposed BurstBiRank and the outperformance of traditional ranking methods. (shrink)

While numerous studies have shown diverse effects of rankings, rather little is known about their production. This article contributes to a broader understanding of rankings in society, and does so by focusing on underlying worldviews. I argue that the existence of a ranking and its concrete methodology can be explained by the producer’s paradigmatic assumptions about a world-to-be-ranked. Referring to the sociology of knowledge and studies on commensuration, comparisons, quantification and valuation, I provide a general heuristic to analyze this (...) relation between underlying worldviews and observational regimes through which order is constructed systematically. Presenting empirical results on a ranking for the most famous artists in the world, I show how the review device’s initial problem and its construction of order derive from consistent assumptions about contemporary art, its symbolic structures and its social embeddedness. These findings have implications for both research on rankings and sociology of the arts. (shrink)

Borovik proposed an axiomatic treatment of Morley rank in groups, later modified by Poizat, who showed that in the context of groups the resulting notion of rank provides a characterization of groups of finite Morley rank [2]. (This result makes use of ideas of Lascar, which it encapsulates in a neat way.) These axioms form the basis of the algebraic treatment of groups of finite Morley rank undertaken in [1].There are, however, ranked structures, i.e., structures on which (...) a Borovik-Poizat rank function is defined, which are not ℵ0-stable [1, p. 376]. In [2, p. 9] Poizat raised the issue of the relationship between this notion of rank and stability theory in the following terms: “… ungroupede Borovik est une structure stable, alors qu'un univers rangé n'a aucune raison de l'être …” (emphasis added). Nonetheless, we will prove the following:Theorem 1.1.A ranked structure is superstable.An example of a non-ℵ0-stable structure with Borovik-Poizat rank 2 is given in [1, p. 376]. Furthermore, it appears that this example can be modified in a straightforward way to give ℵ0-stable structures of Borovik-Poizat rank 2 in which the Morley rank is any countable ordinal (which would refute a claim of [1, p. 373, proof of C.4]). We have not checked the details. This does not leave much room for strenghthenings of our theorem. On the other hand, the proof of Theorem 1.1 does give a finite bound for the heights of certain trees of definable sets related to unsuperstability, as we will see in Section 5. (shrink)

In this paper we study the algebraic structure ofω-stable bilinear maps, arbitrary rings, and nilpotent groups. We will also provide rather complete structure theorems for the above structures in the finite Morley rank case.

Minimality ranks in the style of Deissler are one way of measuring the structural complexity of minimal extensions of first-order structures. In particular, positive Deissler rank measures the complexity of the injective envelope of a module as an extension of that module. In this paper we solve a problem of the second author by showing that certain injective envelopes have the maximum possible positive Deissler rank complexity. The proof shows that this complexity naturally reflects the internal structure of the (...) injective extension in the form of the levels of the Matlis hierarchy. (shrink)

There are several approaches implementing reasoning based on conditional knowledge bases, one of the most popular being System Z (Pearl, Proceedings of the 3rd conference on theoretical aspects of reasoning about knowledge, TARK ’90, Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, pp. 121–135, 1990). We look at ranking functions (Spohn, The Laws of Belief: Ranking Theory and Its Philosophical Applications, Oxford University Press, Oxford, 2012) in general, conditional structures and c-representations (Kern-Isberner, Conditionals in Nonmonotonic Reasoning and Belief Revision: (...) Considering Conditionals as Agents, vol. 2087 of LNCS, Springer, Berlin, 2001) in order to examine the reasoning strength of the different approaches by learning which of the known calculi of nonmonotonic reasoning (System P and R) and Direct Inference are applicable to these inference relations. Furthermore we use the recently proposed Enforcement-postulate (Kern-Isberner and Krümpelmann, Proceedings of the 22nd international joint conference on artificial intelligence, vol. 2, IJCAI’11, AAAI Press, pp. 937–942, 2011) to show dependencies between these approaches. (shrink)

Let L be a countable language, let I be an isomorphism-type of countable L-structures, and let a∈2ω. We say that I is a-strange if it contains a computable-from-a structure and its Scott rank is exactly ω1a. For all a, a-strange structures exist. Theorem : If C is a collection of ℵ1 isomorphism-types of countable structures, then for a Turing cone of a’s, no member of C is a-strange.

The implementation of the UN Sustainable Development Goals and the Lisbon Strategy sets the task of a comprehensive study of the citizens` well-being, determining the state and trends in the level and quality of life not only by traditional methods of social statistics, but also through comprehensive sociological research. This approach has significant advantages since it allows us to generalize the state of social development of a society based on the population`s opinions, to study the emerging social risks that concern (...) the population, to determine the differentiation of countries by indicators of well-being. The foundations of the new approach to the analysis of social processes were laid by the scientific achievements of the 60s of the last century. The dominant paradigm was the economic goals and parameters of statistically measured national income, household income, wages and their differentiation. The environmental risks that threaten the future of civilization were identified and analyzed in the 70s of the XX century. The production contradiction, which raised the question of measuring the quality of life in a new way, was articulated. The economic component was mixed and replaced with the welfare parameter. The sustainable development, including the indicators of well-being, the fight against poverty, and the environment were declared to be the goals of the society. The tasks of monitoring the solution of these problems are solved by sociological research, whose mathematical formalization can become a structural element of economic and mathematical modeling of social processes. (shrink)

Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which extended (...) causal models with their two modalities can be subsumed under so called which contain just one modality. These two constraints will be formally precise versions of Lewissystem of weights or priorities” governing overall similarity between possible worlds. (shrink)

We develop a model of Disappointment in which disappointment and elation arise from comparing the outcome received, not with an expected value as in previous models, but rather with the other individual outcomes of the lottery. This approach may better reflect the way individuals are liable to experience disappointment. The model obtained accounts for classic behavioral deviations from the normative theory, offers a richer structure than previous disappointment models, and leads to a Rank-Dependent Utility formulation in a transparent way. Thus, (...) our disappointment model may provide a clear psychological rationale for the subjective transformation of probabilities. (shrink)

Meets what? Ranking theory is, as far as I know, the only existing theory suited for underpinning Keith Lehrer’s account of knowledge and justification. If this is true, it’s high time to bring both together. This is what I shall do in this paper. However, the result of defining Lehrer’s primitive notions in terms of ranking theory will be disappointing: justified acceptance will, depending on the interpretation, either have an unintelligible structure or reduce to mere acceptance, and in the latter (...) interpretation knowledge will reduce to true belief. Of course, this result will require a discussion of who should be disappointed. So, the plan of the paper is simple: In section 1 I shall briefly state what is required for underpinning Lehrer’s account and why most of the familiar theories fail to do so. In section 2 I shall briefly motivate and introduce ranking theory. Basing Lehrer’s account on it will be entirely straightforward. Section 3 proves the above-mentioned results. Section 4, finally, discusses the possible conclusions. (shrink)

A structure (M, $ ,...) is called quasi-o-minimal if in any structure elementarily equivalent to it the definable subsets are exactly the Boolean combinations of 0-definable subsets and intervals. We give a series of natural examples of quasi-o-minimal structures which are not o-minimal; one of them is the ordered group of integers. We develop a technique to investigate quasi-o-minimality and use it to study quasi-o-minimal ordered groups (possibly with extra structure). Main results: any quasi-o-minimal ordered group is abelian; any (...) quasi-o-minimal ordered ring is a real closed field, or has zero multiplication; every quasi-o-minimal divisible ordered group is o-minimal; every quasi-o-minimal archimedian densely ordered group is divisible. We show that a counterpart of quasi-o-minimality in stability theory is the notion of theory of U-rank 1. (shrink)

This paper establishes a conjecture of Steel [7] regarding the structure of elementary embeddings from a level of the cumulative hierarchy into itself. Steel’s question is related to the Mitchell order on these embeddings, studied in [5] and [7]. Although this order is known to be illfounded, Steel conjectured that it has certain large wellfounded suborders, which is what we establish. The proof relies on a simple and general analysis of the much broader class of extender embeddings and a variant (...) of the Mitchell order called the internal relation. (shrink)

The purpose of this article is to delineate the process of evolution of know­ledge organization systems (KOSs) through identification of principles of unity such as internal and external unity in organizing the structure of KOSs to achieve content storage and retrieval purposes and to explain a novel method used in ranking of KOSs by proposing the principle of rank unity. Different types of KOSs which are addressed in this article include dictionaries, Roget’s thesaurus, thesauri, micro, macro, and meta-thesaurus, ontologies, and (...) lower, middle, and upper-level ontologies. This article relied on dialectic models to clarify the ideas in Kant’s know­ledge theory. This is done by identifying logical relationships between categories (i.e., Thesis, antithesis, and synthesis) in the creation of data, information, and know­ledge in the human mind. The Analysis has adapted a historical methodology, more specifically a documentary method, as its reasoning process to propose a conceptual model for ranking KOSs. The study endeavors to explain the main elements of data, information, and know­ledge along with engineering mechanisms such as data, information, and know­ledge engineering in developing the structure of KOSs and also aims to clarify their influence on content storage and retrieval performance. KOSs have followed related principles of order to achieve an internal order, which could be examined by analyzing the principle of internal unity in know­ledge organizations. The principle of external unity leads us to the necessity of compatibility and interoperability between different types of KOSs to achieve semantic harmonization in increasing the performance of content storage and retrieval. Upon introduction of the principle of rank unity, a ranking method of KOSs utilizing cognition states as criteria could be considered to determine the position of each know­ledge organization with respect to others. The related criteria of the principle of rank unity- cognition states- are derived from Immanuel Kant’s epistemology. The research results showed that KOSs, while having defined positions in cognition states, specific principles of order, related operational mechanisms, and related principles of unity in achieving their specific purposes, have benefited from the developmental experiences of previous KOSs, and further, their developmental processes owe to the experiences and methods of their previous generations. (shrink)

Sustainable development calls for choices among alternative policy options. It is a common view that such choices can be justified by appealing to an evaluative ranking of the options with respect to how their consequences affect a broad range of prudential and moral values. Three philosophically motivated proposals for analysing evaluative rankings are discussed: the measured merits model (e.g. Chang), the ordered values model (e.g. Griffin), and the permissible preference orderings model (Rabinowicz). The analysis focuses on the models’ potential for (...) making transparent how an evaluative ranking can contribute to a justified choice among options, particularly in situations that involve diverse values as typically found in debates on sustainable development. Such transparency plays a crucial role when policy rankings are going to be used as arguments in political decision processes. The measured merits model is found to have questionable consequences for the concept of sustainability, while the ordered values model calls for an axiological framework that cannot plausibly be spelled out for sustainability. The permissible preference orderings model is more promising. Its formal structure and its ability to deal with value-pluralism provide an interesting re-structuring of the problem of justifying choices in sustainability issues. (shrink)

Workplace incivility is a common phenomenon that is frequently found across all organizations and cultures. This study was planned to investigate the impact of workplace incivility on job and non-job related gossips through the mediating role of cynicism and psychological contract violation. The perspective of low-ranked unionized employees was explored through a survey method by using stratified sampling in eight strata, which were formulated based on geographical distribution. A total of four hundred questionnaires were distributed among the employees of (...) eight circles, 50 from each, while use able responses remained 301. SmartPLS was used to analyze the data through structural equation modeling. From a theoretical perspective, this study has made several contributions by investigating the impact of workplace incivility in the South Asian context and documenting the impact of incivility from the perspective of individuals belonging to minority socio-cultural status. Besides supporting existing literature, this study provided a unique argument that low-ranked employees in South Asian societies do not spread nonjob-related gossips. This finding is contradictory to the existing literature; and, thus, calls for future research to identify this inconsistency. Limitations and future directions are also discussed. (shrink)

We understand from the oldest sources that have reached us that according to their status, racial characteristics, culture, religion etc. people called their adressees with many different names besides their own names. The Arabic nicknames and titles, which are the main subject of our research result of this necessity. Before the formation of Islamic culture and civilization, different titles were used in all civilizations, especially in the Byzantine and Sassanid empires, for the members of the group, which were considered as (...) the elite class, apart from their names. Of course, the Arab society of jahiliyyah was also greatly influenced by his. In the political and bureaucratic structure created by the rapid spread of Islam and the interaction from different civilizations, a new naming, or rather nicknames, were made by using religious figures. This happened to such extend that the original names of many rulers remained in the shadows. The strict centralist structure of the Umayyad state required an authoritarian state administration that would not need excessive credit or definition. Therefore, the caliph did not need an extra nickname or title to define himself. At the same time, it would be appropriate to say that they never had any thoughts of praising the politicians and bureaucrats affiliated with them. The radical change in the political understanding with the Abbasid revolution also led to a great change in naming strategies. In fact, it is possible to explain the differentiation in this management approach through titles in the shortest way. The famous names of the Abbasid caliphs are nothing but nicknames. These names, which are adorned with the words of Allah, are actually an effort to show religious sensitivity to the subjects. The sensitivity in the language of diplomacy has come to the fore even more with the special divans established. The language of religion and the language of politics have been intertwined, and the caliph, who is the representative of the creator on earth, has been giving nicknames/titles around him. We see the actual situation of this practice as concrete in relation to the vassal states. During the Abbasid period, the level of relations between the states, which first emerged as semi-independent and later independent, and the caliphate differed according to time and conditions. In proportion to the political power of the Abbasid state, these heads of state were given different ranks. In this research, we try to reveal the background of the ranks given to the heads of vassal state established in the Khorasan and Transoxiana region and carrying out very important activities in the political sense. Additionally, we aim reveal to find out the political, religious and social structure of Tahirids, Saffarids, and Samanids, who are also very important in terms of Turkish history and serve as a bridge between the region and the center of the caliphate, Baghdad. We think that the subject discussed is important in order to discover the unknown aspects of the historical process in the political and bureaucratic formation of the Turkish empires established after the collapse of these three vassal states. In fact, it can be said that even today, the historical anatomy of the ranks used in terms of status determination and the arrangement of the political field in different Islamic geographies is being explored. Most importantly, in this study, we try discover the cornerstones of the communication dimension of the mawali with the Arab power. The location of the Transoxiana and Khorasan geographies before the Islamic conquests and the population fluidity accelerated by the Turkish migrations were an important factor in the political formation of the region during the Abbasid period. The historical background was taken into consideration in the titles given to the vassal state rulers. It is remarkable that the caliph gave the old Turkish title “ıhsid” to a Turkish leader of a state established in Egypt. There are many other examles such as this with regard to the vassal states in the East. The conclusion we have obtained from our study is that titles play a decisive role in the political connection between the center of the caliphate and the affiliated states. On the one hand, this regulates the balance between the center and local administrators, on the other hand, it determines the moral as well as the material rank of the sultans in the eyes of the people. In fact, the successes in the conquests led the caliphs to rank the vassal sultans with titles. This situation is a kind of password that determines the balance between the religious authority, the caliphate, and the worldly authority. (shrink)

Makkai [10] produced an arithmetical structure of Scott rank $\omega _{1}^{\mathit{CK}}$. In [9]. Makkai's example is made computable. Here we show that there are computable trees of Scott rank $\omega _{1}^{\mathit{CK}}$. We introduce a notion of "rank homogeneity". In rank homogeneous trees, orbits of tuples can be understood relatively easily. By using these trees, we avoid the need to pass to the more complicated "group trees" of [10] and [9]. Using the same kind of trees, we obtain one of rank (...) $\omega _{1}^{\mathit{CK}}$ that is "strongly computably approximable". We also develop some technology that may yield further results of this kind. (shrink)

We calculate the possible Scott ranks of countable models of Peano arithmetic. We show that no non-standard model can have Scott rank less than $\omega $ and that non-standard models of true arithmetic must have Scott rank greater than $\omega $. Other than that there are no restrictions. By giving a reduction via $\Delta ^{\mathrm {in}}_{1}$ bi-interpretability from the class of linear orderings to the canonical structural $\omega $ -jump of models of an arbitrary completion T of $\mathrm {PA}$ we (...) show that every countable ordinal $\alpha>\omega $ is realized as the Scott rank of a model of T. (shrink)

We model a piece of text of human language telling a story by means of the quantum structure describing a Bose gas in a state close to a Bose–Einstein condensate near absolute zero temperature. For this we introduce energy levels for the words used in the story and we also introduce the new notion of ‘cogniton’ as the quantum of human thought. Words are then cognitons in different energy states as it is the case for photons in different energy states, (...) or states of different radiative frequency, when the considered boson gas is that of the quanta of the electromagnetic field. We show that Bose–Einstein statistics delivers a very good model for these pieces of texts telling stories, both for short stories and for long stories of the size of novels. We analyze an unexpected connection with Zipf’s law in human language, the Zipf ranking relating to the energy levels of the words, and the Bose–Einstein graph coinciding with the Zipf graph. We investigate the issue of ‘identity and indistinguishability’ from this new perspective and conjecture that the way one can easily understand how two of ‘the same concepts’ are ‘absolutely identical and indistinguishable’ in human language is also the way in which quantum particles are absolutely identical and indistinguishable in physical reality, providing in this way new evidence for our conceptuality interpretation of quantum theory. (shrink)

The ideal of mathematical exactness is strongly paradigmatic for modern science, for which Mathematics practically functions as a metaphysical foundation. This strongly influenced Philosophy. In our century, however, critical voices arise, even from the ranks of scientists. Reflection on the foundations of Mathematics has produced a deeper insight into its nature. The tendency to judge content by structure becomes less predominant. Metaphysics is no longer rejected as only producing constructions with unjustified claims to necessity. This book combines contemporary Philosophy of (...) Mathematics with classical philosophical themes. It replaces the anti-metaphysical tendencies of modern and postmodern Philosophy by an unrestricted horizon of epistemic perspectives. (shrink)

The research presented in this paper was motivated by our aim to study a problem due to J. Bourgain [3]. The problem in question concerns the uniform boundedness of the classical separation rank of the elements of a separable compact set of the first Baire class. In the sequel we shall refer to these sets (separable or non-separable) as Rosenthal compacta and we shall denote by ∝(f) the separation rank of a real-valued functionfinB1(X), withXa Polish space. Notice that in [3], (...) Bourgain has provided a positive answer to this problem in the case ofKsatisfyingwithXa compact metric space. The key ingredient in Bourgain's approach is that whenever a sequence of continuous functions pointwise converges to a functionf, then the possible discontinuities of the limit function reflect a local ℓ1-structure to the sequence (fn)n. More precisely the complexity of this ℓ1-structure increases as the complexity of the discontinuities offdoes. This fruitful idea was extensively studied by several authors (c.f. [5], [7], [8]) and for an exposition of the related results we refer to [1]. It is worth mentioning that A.S. Kechris and A. Louveau have invented the rank rND(f) which permits the link between thec0-structure of a sequence (fn)nof uniformly bounded continuous functions and the discontinuities of its pointwise limit. Rosenthal'sc0-theorem [11] and thec0-index theorem [2] are consequences of this interaction.Passing to the case where either (fn)nare not continuous orXis a non-compact Polish space, this nice interaction is completely lost. (shrink)

Scholarship on gender and policing has frequently applied gendered organizational theory to understand how this type of organization and the men who run it produce gendered difference and inequity at the workplace. In this article, I draw on ethnographic research on lower ranked policewomen in Pakistan and contend that to fully fathom women’s marginalization at work, an analysis must not limit itself to the organization or the men who create the inequity but must also focus on women’s workplace behavior. (...) My research sheds light on women’s anxieties about working with a large number of men and about people questioning their morality and character because they do so. I also demonstrate how their subsequent coping strategies can impede their professional development and reproduce their marginalization at their workplace. This woman-centric approach, which examines how policewomen navigate gendered landscapes in different patriarchal social spaces, therefore shows that workplace inequity is the collective result of the interplay between different actors and social structures, and leads to a more complex understanding of this phenomenon. (shrink)

Research in anthropology has shown that kin terminologies have a complex combinatorial structure and vary systematically across cultures. This article argues that universals and variation in kin terminology result from the interaction of (1) an innate conceptual structure of kinship, homologous with conceptual structure in other domains, and (2) principles of optimal, “grammatical” communication active in language in general. Kin terms from two languages, English and Seneca, show how terminologies that look very different on the surface may result from variation (...) in the rankings of a universal set of constraints. Constraints on kin terms form a system: some are concerned with absolute features of kin (sex), others with the position (distance and direction) of kin in “kinship space,” others with groups and group boundaries (matrilines, patrilines, generations, etc.). Also, kin terms sometimes extend indefinitely via recursion, and recursion in kin terminology has parallels with recursion in other areas of language. Thus the study of kinship sheds light on two areas of cognition, and their phylogeny. The conceptual structure of kinship seems to borrow its organization from the conceptual structure of space, while being specialized for representing genealogy. And the grammar of kinship looks like the product of an evolved grammar faculty, opportunistically active across traditional domains of semantics, syntax, and phonology. Grammar is best understood as an offshoot of a uniquely human capacity for playing coordination games. (shrink)

Based on the work done in [][] in the o‐minimal and geometric settings, we study expansions of models of a supersimple theory with a new predicate distiguishing a set of forking‐independent elements that is dense inside a partial type, which we call H‐structures. We show that any two such expansions have the same theory and that under some technical conditions, the saturated models of this common theory are again H‐structures. We prove that under these assumptions the expansion is (...) supersimple and characterize forking and canonical bases of types in the expansion. We also analyze the effect these expansions have on one‐basedness and CM‐triviality. In the one‐based case, when T has SU‐rank and the SU‐rank is continuous, we take to be the type of elements of SU‐rank and we describe a natural “geometry of generics modulo H” associated with such expansions and show it is modular. (shrink)

This study investigates structural influence of the Madrassah system on effectiveness of its students in terms of civic health, system thinking and professional development. The researchers constructed the instrument of survey after rigorous literature review, frequent interaction with scholars, clerics and policy makers. The survey was administrated to 600 Madrassah’s students from different schools of thought. By applying T-test and Kruskal Waliss Rank Test for measurement of effectiveness and Structural Equation Modeling methodology the researchers has explored the relationship between the (...) variables, and later analyzed with the help of selected model. Findings of the study demonstrate that education system followed in Madrassahs does not seem to be effective and need-based in contemporary times. Indicators of Madrassah structure such as curriculum and openness negatively influences the students while peda­gogy positively influences the effectiveness of students of Madrasah in Pakistan. In the end, it is recommended that curriculum and pedagogy of Madrassah should be reformed and updated in accordance with knowledge-based economy. This will not only upgrade the poor segment of society but also bring together the variety of individuals close enough to understand each other. (shrink)

Let K be a family of structures, closed under isomorphism, in a fixed computable language. We consider effective lists of structures from K such that every structure in K is isomorphic to exactly one structure on the list. Such a list is called a computable classification of K, up to isomorphism. Using the technique of Friedberg enumeration, we show that there is a computable classification of the family of computable algebraic fields and that with a 0'-oracle, we can (...) obtain similar classifications of the families of computable equivalence structures and of computable finite-branching trees. However, there is no computable classification of the latter, nor of the family of computable torsion-free abelian groups of rank 1, even though these families are both closely allied with computable algebraic fields. (shrink)

We introduce the concepts of Morley rank and Morley degree for structures based on Banach spaces. We characterize ω-stability in terms of Morley rank, and prove the existence of prime models for ω-stable theories.

A magisterial work in the grand tradition of systematic philosophy not seen in this country perhaps since Alfred North Whitehead’s _Process and Reality _, this book by a leading German philosopher aims to resurrect systematic philosophy as an essential part of the theoretical enterprise. In Lorenz Puntel’s vision, philosophy as the universal science can be holistic without being imperialistic. The book presents theoretical frameworks as indispensable for any and all theorizing. It argues that there can be truths only relative to (...) sufficiently determinable theoretical frameworks, and that all such frameworks are genuinely revelatory ontologically. No problematic relativism results, however, because such frameworks can be compared and thereby ranked with respect to their theoretical adequacy. _Structure and Being _contributes to the reconciliation of analytic and continental philosophy by insisting upon clarity and precision, as the former does, while aiming for comprehensiveness, as the latter often does. (shrink)

Jones argues that extending Seneca kin terms to second cousins requires a revised version of Optimality Theoretic grammar. I extend Seneca terms using three constraints on expression of markers in nested binary classification trees. Multiple constraint rankings on a nested set coupled with local parity checking determines how a given kin classification grammar marks structural endogamy.