In this paper we discuss the following contributions to recursion theory made by John Myhill: two sets are recursively isomorphic iff they are one-one equivalent; two sets are recursively isomorphic iff they are recursively equivalent and their complements are also recursively equivalent; every two creative sets are recursively isomorphic; the recursive analogue of the Cantor–Bernstein theorem; the notion of a combinatorial function and its use in the theory of recursive equivalence types.

In this paper we generalize the pigeonhole principle by using isols as our fundamental counting tool.

In this paper we present a contribution to a classical result of E. Ellentuck in the theory of regressive isols. E. Ellentuck introduced the concept of a hyper-torre isol, established their existence for regressive isols, and then proved that associated with these isols a special kind of semi-ring of isols is a model of the true universal-recursive statements of arithmetic. This result took on an added significance when it was later shown that for regressive isols, the property of (...) being hyper-torre is equivalent to being hereditarily odd-even. In this paper we present a simplification to the original proof for establishing that equivalence. (shrink)

In this paper we present an equivalence between the category of commutative regular rings and the category of Boolean-valued fields, i.e., Boolean-valued sets for which the field axioms are true. The author used this equivalence in [12] to develop a Galois theory for commutative regular rings. Here we apply the equivalence to give an alternative construction of an algebraic closure for any commutative regular ring.Boolean-valued sets were developed in 1965 by Scott and Solovay [10] to simplify independence proofs in set (...) theory. They later were applied by Takeuti [13] to obtain results on Hilbert and Banach spaces. Ellentuck [3] and Weispfenning [14] considered Boolean-valued rings which consisted of rings and associated Boolean-valued relations. To the author's knowledge, the present work is the first to employ the Boolean-valued sets of Scott and Solovay to obtain results in algebra.The idea that commutative regular rings can be studied by examining the properties of related fields is not new. For several years algebraists and logicians have investigated commutative regular rings by representing a commutative regular ring as a subdirect product of fields or as the ring of global sections of a sheaf of fields over a Boolean space. These representations depend, as does the work presented here, on the fact that the set of central idempotents of any ring with identity forms a Boolean algebra. The advantage of the Boolean-valued set approach is that the axioms of classical logic and set theory are true in the Boolean universe. Therefore, if the axioms for a field are true for a Boolean-valued set, then other properties of the set can be deduced immediately from field theory. (shrink)

Interpretation of the classics in political theory seems to go in waves. For a while we had John Locke, the bourgeois thinker. Now we seem to be in a Locke-as-radical-democrat phase. Locke-the-bourgeois had problems of its own, but a radically democratic Locke -- not just the old Locke as liberal democrat but Locke as quasi-Leveller -- strains the interpretative imagination more than most; yet in recent years, several different kinds of argument have been advanced in support of it, both textual (...) and contextual. The most effective argument has proceeded by situating Locke in the context of radical Whig politics in the 1670s and '80s, the struggles over religious toleration and the royal succession, in particular the �Exclusion Crisis� of 1679-81. This contextual argument has been accompanied by various textual interpretations having to do with Locke's conceptions of property, consent, representation, the right of revolution and natural law. Among other things, these are supposed to show that while Locke had nothing explicit to say about the extent of the franchise, the weight of evidence suggests that he would have supported a fairly wide franchise, perhaps even something like the (almost) manhood suffrage advocated by the Levellers (at least according to some, and probably the most convincing, interpretations of their ideas). Most recently, in these pages, Martin Hughes, building on the work of James Tully and Richard Ashcraft in particular, has pushed the argument as far as it can probably go. His argument on taxation and suffrage has provided a motivation here for a wider exploration of Locke's views on representation, consent and the franchise. (shrink)

This study focuses on the spatialization and institutionalization of social networks of Russian women who migrated to Turkey via marriage in the last 30 years. Specifically, it investigates how and why their social networks have been changing at the local and transnational levels. We conducted in-depth interviews with 56 women between 2014−2021. Our extensive analysis indicates that despite their newly established status via marriages, the Russian women have weak ties with the locals regardless of the migration period, preferring mostly to (...) engage with other Russian women in Turkey. Even if the different migrant associations established by Russian migrants in Turkey do not actually aim this, they create an effect that increases the social distance with the host society and serves to strengthen the connection between the migrants. Also, unlike pioneer migrants, newer marriage migrants have established strong transnational ties with others living overseas, regardless of their gender or ethnic identity. Further, this study reveals that the migrant women's subjectivity, their spouses’ benefit-oriented negotiation styles, and the state's diaspora policy all shape the women's social networks at different levels. (shrink)

Decisions related to animal welfare standards depend on farmer’s multiple goals and values and are constrained by a wide range of external and internal forces. The aim of this paper is twofold, i.e., to develop a theoretical framework for farmers’ AW decisions that incorporates farmers’ goals, use and non-use values and to present an approach to empirically implement the theoretical framework. The farmer as a head of the farm household makes choices regarding production to maximize the utility of the household. (...) The overall utility of the farmer is determined by his multiple objectives. For the analysis of multi-objective problems, the multiple criteria decision - making paradigm provides an appropriate theoretical framework. However, theories from the field of social-psychology are needed to facilitate the identification of all relevant aspects in the decision making. The practical use of the conceptual framework is demonstrated using a simple numerical application of a multi-objective programming model. Two workshops were devoted to examining the scientific consistency and the practical usefulness of the approach. Implementing this approach will increase knowledge of the main factors and barriers that determine farmers’ decisions with regard to AW standards. This knowledge is relevant during the development of new AW concepts that aims to supply products that comply with above-legal AW standards for middle-market segments. (shrink)

In the fourth section of Goethe’s Zahme Xenien we find the quatrain from which I have taken the theme of such an old and new controversy, which, as I hope, concerns both Germanic studies and the other humanities: “What was it that kept you from us so apart?” I always read Plutarch again and again. “And what was the lesson he did impart?” “They were all human beings—so much is plain.”1 In the very years when Goethe wrote these lines, that (...) is in the 1820s, Hegel repeatedly gave his lectures on the philosophy of history. Right at the beginning he formulated the opposite view which I should like briefly to characterize as “cultural relativism.”Every age has such peculiar circumstances, such individual conditions that it must be interpreted, and can only be interpreted, by reference to itself…. Nothing is shallower in this respect than the frequent appeal to Greek and Roman example which so often occurred among the French at the time of their Revolution. Nothing could be more different than the nature of these peoples and the nature of our own times.2 What is at issue here is not, of course, Hegel’s assertion that ages and peoples differ from each other. We all know that, and Goethe, the attentive reader and traveler, also knew, for instance, that the Roman carnival differed in its character from the celebrations of the Feast of Saint Rochus at Bingen, both of which he had described so lovingly. What makes the cultural historian into a cultural relativist is only the conclusion which we saw Hegel draw, that cultures and styles of life are not only different but wholly incommensurable, in other words that it is absurd to compare the peoples of a region or an age with human beings of other zones because there is no common denominator that would justify us in doing so. 1. ‘Was hat dich nun von uns entfernt?’ Hab immer den Plutarch gelesen. ‘Was has du den dabei gelernt?’ Sind eben alles Menschen gewesen.’ Johann Wolfgang von Goethe, Sämtlich Werke. Jubiläums-ausgabe in 40 Bänden 4:73; with commentary.2. See Georg Wilhelm Friedrich Hegel, Vorselungen über die Philosophie der Geschichte, Werke, 20 vols. , 12:17. E. H. Gombrich was director of the Warburg Institute and Professor of the History of the Classical Tradition at the University of London from 1959 to 1976. His many influential works include The Story of Art, Art and Illusion, Meditations on a Hobby Horse, The Sense of Order, Ideals and Idols, The Image and the Eye, Tributes, Aby Warburg, and New Light on Old Masters. His previous contributions to Critical Inquiry include “The Museum: Past, Present and Future” , “Standards of Truth: The Arrested Image and the Moving Eye” , and “Representation and Misrepresentation”. (shrink)

For the good that I would, I do not; but the evil which I would not, that I do. Now if I do that I would not, it is no more I that do it, but sin that dwelleth in me. Romans 7.19-20.

The failure of the critics of corporate governance to agree on what should be done to improve the governance process can, in most cases, be traced to a different understanding of the role of corporate directors in that process. This article analyzes and contrasts the obligations of directors under two legal theories, the fictional person theory and the organic theory, of the corporation. A comparison of the director's obligations under each theory indicates that the organic theory provides a better basis (...) for assessing the performance of directors and initiating reform.Among the boards of directors of Fortune 500 companies, I estimate that 95% are not fully doing what they are legally, morally, and ethically supposed to do. And they couldn't, even if they wanted to. (shrink)

The chief works of Tacitus and Apuleius have come down to us in a single Beneventan—i.e. South Italian—MS. of the eleventh century. The Annals and Histories of Tacitus, and the Apologia, Metamorphoses, and Florida of Apuleius, depend solely on the authority of the famous Florentine MS. preserved in the Laurentian Library under the press-mark 68.2. Any new light that can be thrown on such a MS. is of interest to classical scholars. With the portion of the MS. containing the works (...) of Tacitus the writer has dealt at some length in a paper read in April, 1913, in London before the International Congress of Historical Studies, which paper will be published shortly. Here it is proposed to deal with the portion containing the works of Apuleius, and with the oldest extant transcript of this portion, which is also in Beneventan writing, and is likewise preserved in the Laurentian Library under the press-mark 29.2. In the critical apparatus of Apuleius Laur. 68.2 is cited as F, and Laur. 29.2 as ø. (shrink)

In R. C. Flickinger's (3rd ed. second impression 1929) we read on pp. 171In the iambic trimeters written by Aeschylus a trisyllabic substitution (tribrach, anapaest or dactyl) for the pure disyllabic iambus occurs only once in about twenty-five verses.Tragic Drama of the Greekstrimeters’ lines like.

Dworkin respondeu afirmativamente à pergunta título do seu texto “Não existe mesmo nenhuma resposta certa em casos controversos?”. Posner criticou Dworkin e respondeu a mesma pergunta negativamente. Discute-se neste artigo as diferentes maneiras como cada filósofo entendeu a pergunta que acarreta diferentes respostas a ela, isto é, de que modo diferenças na concepção do que é o Direito acarretam diferenças a respeito da existência de respostas certas para questões jurídicas.