In this paper, we give an example of a complete computable infinitary theory T with countable models ${\mathcal{M}}$ and ${\mathcal{N}}$ , where ${\mathcal{N}}$ is a proper computable infinitary extension of ${\mathcal{M}}$ and T has no uncountable model. In fact, ${\mathcal{M}}$ and ${\mathcal{N}}$ are (up to isomorphism) the only models of T. Moreover, for all computable ordinals α, the computable ${\Sigma_\alpha}$ part of T is hyperarithmetical. It follows from a theorem of Gregory (JSL 38:460–470, 1972; Not Am Math Soc 17:967–968, 1970) (...) that if T is a Π 1 1 set of computable infinitary sentences and T has a pair of models ${\mathcal{M}}$ and ${\mathcal{N}}$ , where ${\mathcal{N}}$ is a proper computable infinitary extension of ${\mathcal{M}}$ , then T would have an uncountable model. (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)

The 2010 Nagoya Protocol is an international framework for access and benefit sharing (ABS) of the use of genetic and biological resources, with particular focus on indigenous communities. This is especially important in Africa, where local communities have a close reliance on environmental resources and ecosystems. However, national legislation and policies commonly lag behind international agreements, and this poses challenges for legal compliance as well as practical applications. This study reviews the academic literature on the Nagoya Protocol and ABS applications, (...) and then considers the implications of this analysis for research in Africa. Results show that there is uneven engagement with the principles of the Nagoya Protocol across different academic disciplines; local communities are sometimes sidelined in these studies; and only 8% of researchers in the literature analysed are located in Africa. Future developments should focus on ensuring national compliance with the Nagoya Protocol, and that researchers and industry work in partnership with local African communities on ABS issues. (shrink)

Dr. Cyril Bailey and Dr. C. M. Bowra have most recently analysed Virgil's method of using the expressions of Lucretius and Ennius respectively, and Mile A.-M. Guillemin has lately added significant considerations to Father F.-X. M. J. Roiron's long examination of Virgil's method of using again his own former expressions. Since then other work has been done with the purpose of clarifying the less rational part of Virgil's self-repetition; it might be called complementary to the well-known researches of Mr. John (...) Sparrow. With such a purpose I have tried to suggest how Virgil reached the strange phrase in the first Eclogue, rapidum Cretae, or cretae, Oaxen, by a not unparalleled confusion of the names of several different rivers and at least one town. (shrink)

In their political treatises, the scholastic writers Ptolemy of Lucca and Giles of Rome discussed the question of whether women should serve in the military. The dispute came in response to Aristotle, who reported in his Politics that Plato and Socrates taught that women should receive the same military training as men and take an equal part in fighting. Such a treatment was made possible by a medieval context in which women under certain circumstances could be feudal lords responsible for (...) maintaining a contingent of knights and sometimes commanding them, and in which a large number of medieval stories of women fighters or leaders of knights circulated, some of them mythical but others based on real women. Both Giles and Ptolemy ultimately rejected female participation but, in keeping with the dialectical method, proposed arguments on both sides. These involve historical precedent, the biological and medical differences between men and women, analogies between female animals and women, divinely ordained gender roles, and the benefits of exercise. (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.

David Lewis's modal realism claims that nothing can exist in more than one world or time, and that statements about how something would have been are to be analysed in terms of its counterpart. I first explain why the counterpart relation depends on de re modal statements in an intensional language, so that intuitive properties of similarity relations cannot be used to show that the counterpart relation is not an equivalence relation. I then look at test sentences in (the intensional) (...) natural language, and show that none of them provide compelling evidence that a counterpart semantics is needed. (shrink)

These two texts are fundamental for the understanding not only of Neoplatonism but also of the conventions of biography in late antiquity. Neither has received such extensive annotation before in English, and this new commentary makes full use of recent scholarship. The long introduction is intended both as a beginner’s guide to Neoplatonism and as a survey of ancient biographical writing.

Next SectionCultural differences in end-of-life care and the moral disagreements these sometimes give rise to have been well documented. Even so, cultural considerations relevant to end-of-life care remain poorly understood, poorly guided, and poorly resourced in health care domains. Although there has been a strong emphasis in recent years on making policy commitments to patient-centred care and respecting patient choices, persons whose minority cultural worldviews do not fit with the worldviews supported by the conventional principles of western bioethics face a (...) perpetual struggle in getting their care needs met in a meaningful, safe, and healing way. In this essay, attention is given to exploring why cultural differences exist, why they matter, and how health care providers should treat them in order to reduce the incidence and impact of otherwise preventable harmful moral outcomes in end-of-life care. In addressing these questions, a novel application of the renowned terror management theory will be made. (shrink)

In recent years, the non-relativistic quantum dynamics derived from three assumptions; probability current conservation, average energy conservation, and an epistemic momentum uncertainty. Here we show that, these assumptions can be derived from a natural extension of classical statistical mechanics.