In his recent book Scientific Explanation and the Causal Structure of the World Wesley Salmon provides a detailed explanation of objective homogeneity, a concept which is central to his S-R model of explanation. 1 propose a modification of Salmon's definition which both simplifies and (in minor ways) corrects it, while at the same time generalizes it by including an important temporal factor that is missing from the original. I argue that if the world is irreducibly stochastic, then objective probabilities (...) (determined by objective homogeneous reference classes) must be temporally relativized. We can speak coherently of the objective probability of a particular event relative to a given point in time, but not of the objective probability of the event simpliciter. I briefly explore the consequences, of the temporal relativity of objective homogeneity for Salmon's attempt to secure an objective (nonepistemic, nonpraagmatic) S-R basis for causal explanation. (shrink)

A Turing degree d is homogeneous bounding if every complete decidable (CD) theory has a d-decidable homogeneous model A, i.e., the elementary diagram De (A) has degree d. It follows from results of Macintyre and Marker that every PA degree (i.e., every degree of a complete extension of Peano Arithmetic) is homogeneous bounding. We prove that in fact a degree is homogeneous bounding if and only if it is a PA degree. We do this by (...) showing that there is a single CD theory T such that every homogeneous model of T has a PA degree. (shrink)

We define an appropriate analog of the Morley rank in a totally transcendental homogeneous model with type diagram D. We show that if RM[p] = α then for some 1 ≤ n < ω the type p has n, but not n + 1, distinct D-extensions of rank α. This is surprising, because the proof of the statement in the first-order case depends heavily on compactness. We also show that types over (D,ℵ₀)-homogeneous models have multiplicity (Morley degree) (...) 1. (shrink)

In the last five years there have been a number of results about the computable content of the prime, saturated, or homogeneous models of a complete decidable theory T in the spirit of Vaught's "Denumerable models of complete theories" combined with computability methods for degrees d ≤ 0′. First we recast older results by Goncharov, Peretyat'kin, and Millar in a more modern framework which we then apply. Then we survey recent results by Lange, "The degree spectra of homogeneous (...) models," which generalize the older results and which include positive results on when a certain homogeneous model of T has an isomorphic copy of a given Turing degree. We then survey Lange's "A characterization of the 0-basis homogeneous bounding degrees" for negative results about when does not have such copies, generalizing negative results by Goncharov, Peretyat'kin, and Millar. Finally, we explain recent results by Csima, Harizanov, Hirschfeldt, and Soare, "Bounding homogeneous models," about degrees d that are homogeneous bounding and explain their relation to the PA degrees. (shrink)

Much previous study has been done on the degree spectra of prime models of a complete atomic decidable theory. Here we study the analogous questions for homogeneous models. We say a countable model A has a d-basis if the types realized in A are all computable and the Turing degree d can list $\Delta _{0}^{0}$ -indices for all types realized in A. We say A has a d-decidable copy if there exists a model B ≅ A such (...) that the elementary diagram of B is d-computable. Goncharov, Millar, and Peretyat'kin independently showed there exists a homogeneous A with a 0-basis but no decidable copy. We prove that any homogeneous A with a 0'-basis has a low decidable copy. This implies Csima's analogous result for prime models. In the case where all types of the theory T are computable and A is a homogeneous model with a 0-basis, we show A has copies decidable in every nonzero degree. A degree d is 0-homogeneous bounding if any automorphically nontrivial homogeneous A with a 0-basis has a d-decidable copy. We show that the nonlow₂ $\Delta _{2}^{0}$ degrees are 0-homogeneous bounding. (shrink)

In this paper we study elementary submodels of a stable homogeneous structure. We improve the independence relation defined in Hyttinen 167–182). We apply this to prove a structure theorem. We also show that dop and sdop are essentially equivalent, where the negation of dop is the property we use in our structure theorem and sdop implies nonstructure, see Hyttinen.

We study the class of elementary submodels of a large superstable homogeneous model. We introduce a rank which is bounded in the superstable case, and use it to define a dependence relation which shares many (but not all) of the properties of forking in the first order case. The main difference is that we do not have extension over all sets. We also present an example of Shelah showing that extension over all sets may not hold for any (...) dependence relation for superstable homogeneous models. (shrink)

A large homogeneous model M is strongly minimal, if any definable subset is either bounded or has bounded complement. In this case is a pregeometry, where bcl denotes the bounded closure operation. In this paper, we show that if M is a large homogeneous strongly minimal structure and is non-trivial and locally modular, then M interprets a group. In addition, we give a description of such groups.

Goncharov and Peretyat'kin independently gave necessary and sufficient conditions for when a set of types of a complete theory is the type spectrum of some homogeneous model of. Their result can be stated as a principle of second order arithmetic, which is called the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic (...) class='Hi'>Model Theorem (AMT), which states that every complete atomic theory has an atomic model. The authors show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense and do the same for an analogous result of Peretyat'kin giving necessary and sufficient conditions for when a set of types is the type spectrum of some model. (shrink)

The antifloating property of underground structures in areas with high underground water levels is a key design aspect. Evaluating the buoyancy forces acting on underground structures is complicated, particularly in the presence of confined water beneath the structures. Herein, the effects of the permeability coefficient of layered soil, hydraulic gradient, and embedment depth of the aquiclude on the buoyancy force acting on underground structures are investigated through three model tests: calibration of the test system, buoyancy force acting on a (...) structure located in homogeneous soil considering vertical direction seepage, and buoyancy force acting on a structure located in layered soil considering vertical seepage of confined water. The results show that the pore pressure along the structure and the buoyancy force acting on the underground structure considering seepage are greater than those obtained under hydrostatic conditions. The raising ratios of the pore pressure and buoyancy force are equal to the vertical hydraulic gradient when seepage occurs in homogeneous soil. In the presence of confined water, the raising ratio is significantly greater than the hydraulic gradient. In the cases studied herein, the raising ratio is approximately twice the hydraulic gradient. Simplified equations are proposed to calculate the buoyancy force acting on underground structures considering the vertical seepage of confined water. Finally, a finite element analysis is carried out to verify the conclusions obtained from the model test and the rationality of the proposed equations. (shrink)

The results herein form part of a larger project to characterize the classification properties of the class of submodels of a homogeneous stable diagram in terms of the solvability (in the sense of [1]) of the potential isomorphism problem for this class of submodels. We restrict ourselves to locally saturated submodels of the monster model m of some power π. We assume that in Gödel's constructible universe ������, π is a regular cardinal at least the successor of the (...) first cardinal in which ������ is stable. We show that the collection of pairs of submodels in ������ as above which are potentially isomorphic with respect to certain cardinal-preserving extensions of ������ is equiconstructible with 0 # . As 0 # is highly "transcendental" over ������, this provides a very strong statement to the effect that potential isomorphism for this class of models not only fails to be set-theoretically absolute, but is of high (indeed of the highest possible) complexity. The proof uses a novel method that does away with the need for a linear order on the skeleton. (shrink)

We prove a version of a small index property theorem for strong amalgamation classes. Our result builds on an earlier theorem by Lascar and Shelah. We then study versions of the small index property for various non-elementary classes. In particular, we obtain the small index property for quasiminimal pregeometry structures.

We introduce a novel point of view on the “models as mediators” framework in order to emphasize certain important epistemological questions about models in science which have so far been little investigated. To illustrate how this perspective can help answer these kinds of questions, we explore the use of simplified models in high energy physics research beyond the Standard Model. We show in detail how the construction of simplified models is grounded in the need to mitigate pressing (...) epistemic problems concerning the uncertainty inherent in the present theoretical and experimental contexts. (shrink)

We prove that every homogeneously Souslin set is coanalytic provided that either (a) 0long does not exist, or else (b) V = K, where K is the core model below a μ-measurable cardinal.

The options in a decision problem generally have outcomes with common features. Putting aside the common features simplifies deliberations, but the simplification requires a philosophical justification that this book provides.

The concepts of health and disease are crucial in defining the aim and the limits of modern medicine. Accordingly it is important to understand them and their relationship. However, there appears to be a discrepancy between scholars in philosophy of medicine and health care professionals with regard to these concepts. This article investigates health care professionals’ concepts of health and disease and the relationship between them. In order to do so, four different models are described and analyzed: the ideal (...) class='Hi'>model, the holistic model, the medical model and the disjunctive model. The analysis reveals that each model has its pros and cons, and that health care professionals appear to apply more than one models. Furthermore, the models and the way health care professionals’ use them may be helpful for scholars in philosophy of medicine with regard to developing theories and communicating them to health care professionals. (shrink)

The first step of the construction of Nézondet's models of finite arithmetics which are counter-models to Erdös–Woods conjecture is to add to the natural numbers the non-standard numbers generated by one of them, using addition, multiplication and divisions by a natural factor allowed in an ultrapower construction. After a review of some properties of such a structure, we show that the choice of the ultrafilter can be managed, using just the Chinese remainder's theorem, so that a model as desired (...) is obtained as early as at the first time. (shrink)

We give a detailed account of the Algebraically Closed and Existentially Closed members of the second Lee class B 2 of distributive p-algebras, culminating in an explicit construction of the countable homogeneous universal model of B 2. The axioms of Schmid [7], [8] for the AC and EC members of B 2 are reduced to what we prove to be an irredundant set of axioms. The central tools used in this study are the strong duality of Clark and (...) Davey [3] for B 2 and the method of Clark [2] for constructing AC and EC algebras using a strong duality. Applied to B 2, this method transfers the entire discussion into an equivalent dual category X 2 of Boolean spaces which carry a pair of tightly interacting orderings. The doubly ordered spaces of X 2 prove to be much more readily constructed and analyzed than the corresponding algebras in B 2. (shrink)

We generalize the result of non-finite axiomatizability of totally categorical first-order theories from elementary model theory to homogeneous model theory. In particular, we lift the theory of envelopes to homogeneous model theory and develope theory of imaginaries in the case of ω-stable homogeneous classes of finite U-rank.

This paper shows that the relevant logics E and Π′ are strongly sound and complete with regards to a version of the “simplified” Routley-Meyer semantics. Such a semantics for E has been thought impossible. Although it is impossible if an admissible rule of E – the rule of restricted assertion or equivalently Ackermann’s δ-rule – is solely added as a primitiverule, it is very much possible when E is axiomatized in the way Anderson and Belnap did. The simplified (...) semantics for E and Π′ requires unreduced frames. Contra what has been claimed, however, no additional frame component is required over and above what’s required to model other relevant logics such as T and R. It is also shown how to modify the tonicity requirements of theternary relation so as to allow for the standard truth condition for both fusion – the intensional conjunction◦ – as well as the converse conditional ←. (shrink)

We show that a $$ -simplified morass can be added by a forcing with working parts of size smaller than $\kappa $. This answers affirmatively the question, asked independently by Shelah and Velleman in the early 1990s, of whether it is possible to do so.Our argument use a modification of a technique of Mitchell’s for adding objects of size $\omega _2$ in which collections of models – all of equal, countable size – are used as side conditions. In our (...) modification, whilst the individual models are, as in Mitchell’s technique, taken ad hoc from quite general classes, the collections of models are very highly structured, in a way that is somewhat different from, perhaps more stringent than, Mitchell’s original, arguably making the method more wieldy and giving the prospect of further uses with more delicate working parts. (shrink)

Research ethics review is a critical aspect of the research governance framework for human subjects research. This usually requires that research protocols be submitted to a research ethics committee for review and approval. This has led to very rapid developments in the domain of research ethics, as RECs proliferate all over the globe in rhyme with the explosion in human subjects research. The work of RECs has increasingly become elaborate, complex, and in many cases urgent, necessitating supporting rules and procedures (...) of operation. Guidelines for elaborating standard operating procedures for the functioning of RECs have also been proposed. The SOPs of well-placed and well-resourced RECs have tended to pay much attention to details, resulting, as a consequence, in generally long, elaborate, intricate and complex SOPs; a model that can hardly be replicated by other committees, equally under ethics review pressures, but working under much more constraining conditions in resource-destitute environments. In this paper, we looked at the content and length of SOPs from African RECs and compared them to the World Health Organization ’s guidelines as the gold standard. We also looked at the SOPs from the Ethics Review and Consultancy Committee of the Cameroon Bioethics Initiative that we elaborated in a simplified way in 2013, and compared them to the WHO’s guidelines and to the other SOPs. Sixteen SOPs from 14 African countries were collected from various sources. Their average length was of 30 pages. By comparison to the guidance of the WHO, only six of them were found acceptable with more than 70 % of the criteria from the gold standard that were fully described. Among those six, two of them were very long and detailed, while the four remaining SOPs ranged from 16 to 24 pages. The ERCC SOPs are seven pages long but maintain all that is of essence for the rigorous, efficient and timely review of protocols. We are convinced that, because of their brevity, simplicity, clarity and user-friendliness, the ERCC SOPs recommend themselves as a model template to, at least, committees similarly situated and/or circumstanced as the ERCC of the Cameroon Bioethics Initiative is. In fact, brevity, clarity, simplicity and user-friendliness are recognized values. Whatever is brief and clear is better than what is not and saves time. What is simple and user-friendly is better than what is not even though the two have the same aims because it saves both time and mental energy. And if this be true in general, it is even truer of the context and its peculiar constraints that we are addressing. (shrink)

It is shown how to model propositional constants within the simplified Routley-Meyer semantics. Various axioms and rules allowingthe definition of modal operators, implicative negations, enthymematical conditionals, and propositions expressing various infinite conjunctions anddisjunctions are set forth and shown to correspond to specific frame conditions. Two propositional constants which are both often designated as “the Ackermann constant” are shown to capture two such “infinite” propositions: The conjunction of every logical law and the conjunction of every truth – what Anderson (...) and Belnap called the “world” constant. (shrink)

We show that if M is a strongly minimal large homogeneous structure in a countable similarity type and the pregeometry of M is locally modular but not modular, then the pregeometry is affine over a division ring.

This paper shows that the relevant logics E and Π′ are strongly sound and complete with regards to a version of the “simplified” Routley-Meyer semantics. Such a semantics for E has been thought impossible. Although it is impossible if an admissible rule of E  the rule of restricted assertion or equivalently Ackermann’s δ-rule  is solely added as a primitive rule, it is very much possible when E is axiomatized in the way Anderson and Belnap did. The (...) class='Hi'>simplified semantics for E and Π′ requires unreduced frames. Contra what has been claimed, however, no additional frame component is required over and above what’s required to model other relevant logics such as T and R. It is also shown how to modify the tonicity requirements of the ternary relation so as to allow for the standard truth condition for both fusion – the intensional conjunction ◦ – as well as the converse conditional ←. (shrink)

We investigate empirically whether framing in general, and the use of Simplifying Models as a framing tool in particular, has an effect on the way topics are cognitively construed. Existing studies on framing in linguistics have either been theoretical or descriptive. Going beyond such methodologically simple approaches, we use a more rigid test design involving the use of a control group, the construction of test conditions in which different Simplifying Models constitute the major source of variation, the inclusion of independent (...) variables like age and prior knowledge of the subjects, and the use of linear and logistic regression analysis. Our results show that our more rigid methodological approach yields a more reliable image of the effect of Simplifying Models on the way in which people deal with information on a complex topic like sustainable food production. Fleshing out these effects further may in time lead to a better informed construction of communication on complex social topics. (shrink)

It is shown how to model propositional constants within the simplified Routley-Meyer semantics. Various axioms and rules allowing the definition of modal operators, implicative negations, enthymematical conditionals, and propositions expressing various infinite conjunctions and disjunctions are set forth and shown to correspond to specific frame conditions. Two propositional constants which are both often designated as “the Ackermann constant” are shown to capture two such “infinite” propositions: The conjunction of every logical law and the conjunction of every truth –what (...) Anderson and Belnap called the “world” constant. (shrink)

In the present paper we examine very weak modal logics C1, D1, E1, S0.5◦, S0.5◦+(D), S0.5 and some of their versions which are closed under replacement of tautological equivalents (rte-versions). We give semantics for these logics, formulated by means of Kripke style models of the form , where w is a «distinguished» world, A is a set of worlds which are alternatives to w, and V is a valuation which for formulae and worlds assigns the truth-vales such that: (i) for (...) all formulae and all worlds, V preserves classical conditions for truth-value operators; (ii) for the world w and any formula ϕ, V(⬜ϕ,w) = 1 iff ∀x∈A V(ϕ,x) = 1; (iii) for other worlds formula ⬜ϕ has an arbitrary value. Moreover, for rte-versions of considered logics we must add the following condition: (iv) V(⬜χ,w) = V(⬜χ[ϕ/ψ],w), if ϕ and ψ are tautological equivalent. Finally, for C1, D1and E1 we must add queer models of the form in which: (i) holds and (ii') V(⬜ϕ,w) = 0, for any formula ϕ. We prove that considered logics are determined by some classes of above models. (shrink)

This paper continues the work of Priest and Sylvan in Simplified Semantics for Basic Relevant Logics, a paper on the simplified semantics of relevant logics, such as B⁺ and B. We show that the simplified semantics can also be used for a large number of extensions of the positive base logic B⁺, and then add the dualising '*' operator to model negation. This semantics is then used to give conservative extension results for Boolean negation.

Scientific research is almost always conducted by communities of scientists of varying size and complexity. Such communities are effective, in part, because they divide their cognitive labor: not every scientist works on the same project. Philip Kitcher and Michael Strevens have pioneered efforts to understand this division of cognitive labor by proposing models of how scientists make decisions about which project to work on. For such models to be useful, they must be simple enough for us to understand their dynamics, (...) but faithful enough to reality that we can use them to analyze real scientific communities. To satisfy the first requirement, we must employ idealizations to simplify the model. The second requirement demands that these idealizations not be so extreme that we lose the ability to describe real-world phenomena. This paper investigates the status of the assumptions that Kitcher and Strevens make in their models, by first inquiring whether they are reasonable representations of reality, and then by checking the models' robustness against weakenings of these assumptions. To do this, we first argue against the reality of the assumptions, and then develop a series of agent-based simulations to systematically test their effects on model outcomes. We find that the models are not robust against weakenings of these idealizations. In fact we find that under certain conditions, this can lead to the model predicting outcomes that are qualitatively opposite of the original model outcomes. (shrink)

We present a new technique for changing the cofinality of large cardinals using homogeneous forcing. As an application we show that many singular cardinals in [Formula: see text] can be measurable in HOD. We also answer a related question of Cummings, Friedman and Golshani by producing a model in which every regular uncountable cardinal [Formula: see text] in [Formula: see text] is [Formula: see text]-supercompact in HOD.

: The Emotional Perception Model of moral judgment intends to account for experientialism about morality and moral reasoning. In explaining how moral beliefs are formed and applied in practical reasoning, the model attempts to overcome the mismatch between reason and action/desire: morality isn’t about reason for actions, yet moral beliefs, if caused by desires, may play a motivational role in agency. The account allows for two kinds of moral beliefs: genuine moral beliefs, which enjoy a relation to desire, (...) and motivationally inert moral beliefs acquired in ways other than experience. Such etiology-based dichotomy of concepts, I will argue, leads to the undesirable view of cognition as a non-homogeneous phenomenon. Moreover, the distinction between moral beliefs and moral beliefs would entail a further dichotomy encompassing the domain of moral agency: one and the same action might possibly be either genuine moral, or not moral, if acted by individuals lacking the capacity for moral feelings, such as psychopaths. Keywords : Moral Beliefs; Cognitive Homogeneity; Moral Agency; Motivation; Psychopathy Credenze morali e omogeneità cognitiva Riassunto : L’ Emotional Perception Model del giudizio morale offre un approccio esperienzialista alla moralità e al ragionamento morale. Il modello, che propone una spiegazione di come le credenze morali vengano prima formate e poi applicate, intende superare il disallineamento tra ragione e azione/desiderio: la moralità non riguarda le ragioni per agire, tuttavia le credenze morali, se causate dal desiderio o in relazione con esso, svolgono un ruolo motivazionale nell’azione. Questo approccio consente di identificare due tipi di credenza morale: le credenze morali genuine, che trattengono una relazione con il desiderio, e le credenze morali senza relazione alcuna con il desiderio e dunque caratterizzate da inerzia motivazionale. Tale tassonomia, la cui origine è da rintracciare nell’eziologia dei concetti, porta alla sgradita visione della cognizione come fenomeno disomogeneo. Inoltre la distinzione tra credenze morali e credenze morali introdurrebbe una ulteriore possibile dicotomia interna al dominio dell’azione morale: una medesima azione può essere al contempo genuinamente morale oppure no, a seconda che venga agita da un individuo con la capacità di esperire sentimenti morali o da uno che ne sia privo, come nel caso di soggetti psicopatici. Parole chiave : Credenze morali; Omogeneità cognitiva; Agentività morale; Motivazione; Psicopatia. (shrink)

We generalize tools and results from first order stable theories to groups inside a simple stable strongly homogeneous model.

The author proposes a neural-network-based explanation of how a brain might acquire intuitive expertise. The explanation is intended merely to be suggestive and lacks many complexities found in even lower animal brains. Yet significantly, even this simplified brain model is capable of explaining the acquisition of simple skills without developing articulable rules for behavior or a model of the skill domain or an explicit identification of which observables in the environment are necessary for skillful behavior. Furthermore, no (...) memories of prior experiences during the learning phase are explicitly stored and accessed during behavior. The explanation thus calls into doubt many conventional and intuitively reasonable assumptions concerning the learning and production of intuitive expertise. (shrink)