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)

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.

LetEbe a computably enumerable equivalence relation on the setωof natural numbers. We say that the quotient set$\omega /E$realizesa linearly ordered set${\cal L}$if there exists a c.e. relation ⊴ respectingEsuch that the induced structure is isomorphic to${\cal L}$. Thus, one can consider the class of all linearly ordered sets that are realized by$\omega /E$; formally,${\cal K}\left = \left\{ {{\cal L}\,|\,{\rm{the}}\,{\rm{order}}\, - \,{\rm{type}}\,{\cal L}\,{\rm{is}}\,{\rm{realized}}\,{\rm{by}}\,E} \right\}$. In this paper we study the relationship between computability-theoretic properties ofEand algebraic properties of linearly ordered sets realized (...) byE. One can also define the following pre-order$ \le _{lo} $on the class of all c.e. equivalence relations:$E_1 \le _{lo} E_2 $if every linear order realized byE1is also realized byE2. Following the tradition of computability theory, thelo-degrees are the classes of equivalence relations induced by the pre-order$ \le _{lo} $. We study the partially ordered set oflo-degrees. For instance, we construct various chains and anti-chains and show the existence of a maximal element among thelo-degrees. (shrink)

We study the structure of Σ11 equivalence relations on hyperarithmetical subsets of ω under reducibilities given by hyperarithmetical or computable functions, called h-reducibility and FF-reducibility, respectively. We show that the structure is rich even when one fixes the number of properly equation imagei.e., Σ11 but not equation image equivalence classes. We also show the existence of incomparable Σ11 equivalence relations that are complete as subsets of ω × ω with respect to the corresponding reducibility on sets. We study complete Σ11 (...) equivalence relations and show that existence of infinitely many properly Σ11 equivalence classes that are complete as Σ11 sets is necessary but not sufficient for a relation to be complete in the context of Σ11 equivalence relations. (shrink)

Defining the degree of categoricity of a computable structure ${\mathcal{M}}$ to be the least degree d for which ${\mathcal{M}}$ is d-computably categorical, we investigate which Turing degrees can be realized as degrees of categoricity. We show that for all n, degrees d.c.e. in and above 0 (n) can be so realized, as can the degree 0 (ω).

We investigate the complexity of embeddings between bi-embeddable structures. In analogy with categoricity spectra, we define the bi-embeddable categoricity spectrum of a structure A as the family of Turing degrees that compute embeddings between any computable bi-embeddable copies of A; the degree of bi-embeddable categoricity of A is the least degree in this spectrum (if it exists). We extend many known results about categoricity spectra to the case of bi-embeddability. In particular, we exhibit structures without degree of bi-embeddable categoricity, and (...) we show that every degree d.c.e above 0(α) for α a computable successor ordinal and 0(λ) for λ a computable limit ordinal is a degree of bi-embeddable categoricity. We also give examples of families of degrees that are not bi-embeddable categoricity spectra. (shrink)

We study arithmetic and hyperarithmetic degrees of categoricity. We extend a result of E. Fokina, I. Kalimullin, and R. Miller to show that for every computable ordinal $\alpha$, $\mathbf{0}^{}$ is the degree of categoricity of some computable structure $\mathcal{A}$. We show additionally that for $\alpha$ a computable successor ordinal, every degree $2$-c.e. in and above $\mathbf{0}^{}$ is a degree of categoricity. We further prove that every degree of categoricity is hyperarithmetic and show that the index set of structures with (...) degrees of categoricity is $\Pi_{1}^{1}$-complete. (shrink)

A Turing degreedis the degree of categoricity of a computable structure${\cal S}$ifdis the least degree capable of computing isomorphisms among arbitrary computable copies of${\cal S}$. A degreedis the strong degree of categoricity of${\cal S}$ifdis the degree of categoricity of${\cal S}$, and there are computable copies${\cal A}$and${\cal B}$of${\cal S}$such that every isomorphism from${\cal A}$onto${\cal B}$computesd. In this paper, we build a c.e. degreedand a computable rigid structure${\cal M}$such thatdis the degree of categoricity of${\cal M}$, butdis not the strong degree of categoricity (...) of${\cal M}$. This solves the open problem of Fokina, Kalimullin, and Miller [13].For a computable structure${\cal S}$, we introduce the notion of the spectral dimension of${\cal S}$, which gives a quantitative characteristic of the degree of categoricity of${\cal S}$. We prove that for a nonzero natural numberN, there is a computable rigid structure${\cal M}$such that$0\prime$is the degree of categoricity of${\cal M}$, and the spectral dimension of${\cal M}$is equal toN. (shrink)

When Kepler concluded that the orbit of Mars was not a circle, he was led to the belief that the orbit was an oval touching the circle at the apsides and lying within the circle at other points. In the definition of the oval, physical hypotheses played a primary role. Two forces were involved; a tractive force arising from the effect of the solar rays rotating with the sun, and a directing force arising from a natural instinct of the planet (...) itself. The former pushed the planet along the orbit while the latter enabled the planet to steer itself across the stream of the solar vortex in a small epicycle. In adopting this physical theory to determine the oval, Kepler was led into what he himself described as ‘a new labyrinth’. After several attempts to construct the oval, and by progressively eliminating the sources of error from his calculating procedures in order to arrive at an accurate mathematical formulation of the physical hypotheses, he was able to conclude that the oval was inconsistent with the empirical data and the physical theory in need of modification. (shrink)

Dentro de la sociología francesa actual, Gilles Lipovetsky se ha convertido de forma paulatina en uno de los sociólogos con mayor proyección internacional, con sus finos análisis sobre las sociedades postmodernas. En este artículo se plantea una revisión crítica de las principales líneas argumentativas que expone el autor francés. El objetivo es el de reflexionar sobre las limitaciones de su aproximación a los conceptos de postmodernidad, hipermodernidad, y consumo.

Robert E. Butts (1928-1997) was a philosopher and historian of science whose central concerns were the distinction between the rational and the irrational. He viewed scientific rationality as our major defence against the various conditions that encourage witch hunts and similar outbursts of irrationality, with all their attendant pain and terror. Butts saw himself as a pragmatic realist, combining what he took to be the best aspects of logical empiricism with a historically informed pragmatism, deeply appreciative of the methods of (...) science, trying to describe a kind of rationality essential in the struggle to preserve human values. This volume gathers previously unpublished essays and lectures with some previously published, thematically related essays. It includes essays and lectures on philosophical aspects of the European witch hunt, on scientific rationality and methodology, and on the relationships between science and philosophy exhibited in the writings of such historically significant figures as Leibniz, D'Alembert, Hume, Kant, Carnap and Kuhn. (shrink)

In response to rapidly rising health care costs in the United States, federal and state governments and private industry are instituting numerous and diverse cost-containment plans. As devices for coping with a scarcity of resources, such plans present serious challenges to physicians' traditional single-minded devotion to patient welfare. Those which contain costs by directly limiting medical options or by controlling physicians' daily clinical decisions can threaten the quality of medical care by allowing economic authorities to make essentially medical judgments. In (...) contrast, other plans coax compliance by arranging incentives, e.g., offering financial rewards for successful cost containment. While they allow for clinical freedom, these plans create conflicts between physicians' fiduciary obligations to their patients and the competing interests of the payers. Such conflicts arise as physicians try to work within governmental or corporate cost containment policies, and also as they attempt to streamline clinical efficiency. Throughout, issues of justice emerge as physicians seek to reconcile their own patients' claims upon limited common resources with others' equally legitimate claims. (shrink)

I must explain at once that these few pages do not attempt or pretend to be anything like a formal review of the recently published posthumous volume of Professor Bowman with the same title. I am precluded from writing such a review partly by the wide range of problems attacked by the author, partly by my own insufficient familiarity with many of the positions of the most recent physical and natural science which are brought under review. I will therefore confine (...) myself, so far as the strict business of the reviewer is concerned, to the single remark that the editor, Professor J. W. Scott, has discharged his difficult task of preparing the book for publication—no easy matter, as will be seen from his Preface—with equal skill and devotion, and has laid himself open to no worse criticism than that there are less than a dozen obvious slight misprints which have escaped detection, but will readily be detected by a careful reader. What I propose to do in the remarks which follow is simply to indicate the very real importance of the book by saying something as to its main purpose and thesis, and the points where I still feel that there is some difficulty or ambiguity about the writer's position which would, no doubt, have been largely cleared up if he had lived to reconstruct the whole six of his Vanuxem Lectures for publication as he has done the first three. (shrink)

Analyses of the 'food business' expose some of the most fascinating and disturbing characteristics of contemporary capitalism as well as some of the most significant flaws within contemporary academic discourses; deficiencies in diets are the material manifestations of the deficiencies in common analytical and conceptual categories as well as political will. Much of the voluminous recent discourse about sustainable development is similarly flawed. This paper reflects on the connections between the character of contemporary capitalism and allied discourses on globalisation, hunger (...) and sustainable development and argues that these connections require a vigorous ethically informed critique. (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)

Although Professor of Philosophy at Calvin College, Alvin Plantinga has developed a theodicy that is fundamentally Arminian rather than Calvinistic. Anthony Flew, although the son of an Arminian Christian minister, regards the Arminian view of ‘free will’ to be both unacceptable on its own terms and incompatible with classical Christian theism. In this paper I hope to disentangle some of the involved controversy regarding theodicy which has developed between Plantinga and Flew, and between Flew and myself. The major portion of (...) this paper is devoted to showing that Plantinga's theodicy contains some serious flaws and undesirable implications. (shrink)