Let us call an integer part of an ordered field any subring such that every element of the field lies at distance less than 1 from a unique element of the ring. We show that every real closed field has an integer part.

There is more than enough evidence to show that cock-fighting, quail-fighting, and even partridge-fighting were favourite sports among the Greeks , no matter what part of the mediterranean world they inhabited. Whether Romans ever shared these passions is another question altogether. When Saglio contributed his article on cock-fighting to the Dictionnaire des antiquitis grecques et romaines, he limited himself to the transports it caused the Greeks. For this he was reprimanded, obliquely, by Schneider, asserting—but neglecting to support the assertion in (...) detail—that Romans also took a keen interest in Hahnenkämpfe. Subsequently, Magaldi set out to prove the existence of formal ludi gallinarii at Pompeii, while Jennison mustered such evidence as could be found for all three forms of avian combat in Rome. Hence, apparently, it has become the communis opinio that Romans shared the Greeks' taste for these ‘raffish’ amusements. (shrink)

Two criteria for rigid designation are distinguished; one according to which 'e' is rigid if 'e might not have been e' is false and the other according to which 'e' is rigid if it designates the same thing in all possible worlds in which it designates anything at all. Such criteria are not equivalent since 'x could not but be f' is not entailed by 'nothing other than x could be f'. I illustrate the latter lack of entailment.

Catullus 6 is a short poem addressed to a certain Flavius, otherwise unknown. Flavius, so we are told, refuses to say anything about his girlfriend, and the poet can explain this only by assuming that he has taken up with a mistress who is singularly unrefined . It is certainly clear that Flavius is not spending his nights alone; the state of his bedroom proves that much . But, says Catullus, there is no reason for Flavius to remain silent, no (...) matter what folly he is engaging in. He should confide in the poet, whose only wish is to praise him and his mistress in witty verse. (shrink)

In his magisterial Religion und Kultus der Römer Georg Wissowa made the statement that a Roman man or woman seeking a priesthood had, among other things, to be free of physical defects. This has since become the communis opinio, sometimes in the form in which Wissowa expressed it, sometimes involving rather the idea that a priest or priestess could be deposed for such defects acquired after entry into the priesthood, and sometimes embracing both concepts simultaneously.

Feature structures are employed in various forms in many areas of linguistics. Informally, one can picture a feature structure as a sort of tree decorated with information about constraints requiring that specific subtrees be identical (isomorphic). Here I show that this informal picture of feature structures can be used to characterize exactly the class of feature structures under their usual subsumption ordering. Furthermore, once a precise definition of tree is fixed, this characterization makes use only of standard domain-theoretic notions regarding (...) the information borne by elements in a domain, thus removing (or better, explaining) all apparentlyad hoc choices in the original definition of feature structures. In addition, I show how this characterization can be parameterized in order to yield similar characterizations of various different notions of feature structure, including acyclic structures, structures with appropriateness conditions and structures with apartness conditions (used to model path inequations). The generalizations to other notions of feature structure also emphasize that the construction given here is in fact independent of the application to feature structures. (shrink)

A comprehensive, critical evaluation of the ideas of the Italian philosopher Benedetto Croce, including a summary of his life.

Barut showed us how it is possible to get a Poincaré invariant n-body equation with a single time. Starting from the Barut equation for n-free particles, we show how to generalize it when they interact through Dirac oscillators with different frequencies. We then particularize the problem to n=2 and consider the particle-antiparticle system whose frequencies are respectively ω and −ω. We indicate how the resulting equation can be solved by perturbation theory, though the spectrum and its comparison with that of (...) the mesons will be given in another publication. (shrink)

Three classes of decidable discrete linear orders with varying degrees of effectiveness are investigated. We consider how a classical order type may lie in relation to these three classes, and we characterize by their order types elements of these classes that have effective nontrivial self-embeddings.

The Hamiltonian for n relativistic electrons without interaction but in a Coulomb potential is well known. If in this Hamiltonian we take r ′ u =r′, P ′ u =P′ with u=1,2,..., n, we obtain a one-body problem in a Coulomb field, but the appearance of n of the α u , u=1,..., n, each of which corresponds to spin $\tfrac{1}{2}$ , indicates that we may have spins up to (n/2). We analyze this last problem first by denoting the 4×4 (...) matrices α, β as direct products of 2×2 matrices which correspond to the ordinary spin, and a new concept, also related to the SU(2) group, which we call sign spin. In this new notation our problem depends on the sixteen generators of a U(4) group reduced along the chain Û(2)⊗Ŭ(2) sub-groups associated with the ordinary and sign spins. We now make a change of variables in our Hamiltonian so a term ε related to the frequency ω of an oscillator, which will be our variational parameter, appears in it, and later construct the full states of the problem with a harmonic oscillator of frequency 1 and ordinary and sign spin parts. Finally we obtain the matrix representation of our Hamiltonian with respect to the states mentioned and discuss the energy spectra of the problem where the partition {h} representing the irrep of U(4) and j the total angular momentum, take the values {h}=[1], j= $\tfrac{1}{2}$ ; {h}=[11], j=0; {h}=[2], j=0. (shrink)

The Hamiltonian for n relativistic electrons without interaction but in a Coulomb potential is well known. If in this Hamiltonian we take r′u=r′, P′u=P′ with u=1,2,..., n, we obtain a one-body problem in a Coulomb field, but the appearance of n of the αu, u=1,..., n, each of which corresponds to spin\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\tfrac{1}{2}$$ \end{document}, indicates that we may have spins up to (n/2). We analyze this last problem first by denoting the (...) 4×4 matrices α, β as direct products of 2×2 matrices which correspond to the ordinary spin, and a new concept, also related to the SU(2) group, which we call sign spin. In this new notation our problem depends on the sixteen generators of a U(4) group reduced along the chain Û(2)⊗Ŭ(2) sub-groups associated with the ordinary and sign spins. We now make a change of variables in our Hamiltonian so a term ε related to the frequency ω of an oscillator, which will be our variational parameter, appears in it, and later construct the full states of the problem with a harmonic oscillator of frequency 1 and ordinary and sign spin parts. Finally we obtain the matrix representation of our Hamiltonian with respect to the states mentioned and discuss the energy spectra of the problem where the partition {h} representing the irrep of U(4) and j the total angular momentum, take the values {h}=[1], j=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\tfrac{1}{2}$$ \end{document}; {h}=[11], j=0; {h}=[2], j=0. (shrink)

It is well-known that feature structures can be fruitfully viewed as forming a Scott domain. Once a linguistically motivated notion of set value in feature structures is countenanced, however, this is no longer possible inasmuch as unification of set values in general fails to yield a unique result. In Pollard and Moshier 1990 it was shown that, while falling short of forming a Scott domain, the set of feature structures possibly containing set values satisfies the weaker condition of forming a (...) 2/3 SFP domain when equipped with an appropriate notion of subsumption: that is, for any finite setS of feature structures, there is a finite setM of minimal upper bounds ofS such that any upper bound ofS is approximated by a member ofM. Unfortunately, the 2/3 SFP domains are not as pleasant to work with as Scott domains since they are not closed under all the familiar domain constructions; and the question has remained open whether the feature structure domain satisfies the added condition of profiniteness. In this paper we resolve this question in the affirmative. (shrink)

Angels of Death, which reports on Magnusson’s study of the euthanasia underground within the HIV/AIDS communities principally in Sydney, Melbourne, and San Francisco, is, in many respects, a unique work. It is written by a legal scholar but is quite deliberately non-legalistic; indeed, Magnusson makes clear his intention is not to create another manifesto but to inject new perspectives into the euthanasia debate. The book’s underlying methodology also sets it apart. It is based on the author’s own extensive empirical research, (...) drawing on data gathered over three years in the course of indepth, face to face interviews with healthcare workers in Australia and the USA who have been involved in caring for people with AIDS. This kind of empirical research is not often undertaken by lawyers, and while a number of studies into attitudes and practices of healthcare professionals in relation to euthanasia have been carried out by researchers from other disciplines, very few have involved interview based research, relying instead predominantly on surveys.1 By any measure, Magnusson’s research has been undertaken with meticulous care. He is able to balance his gratitude and respect for his interviewees with the need to provide a dispassionate and evenhanded commentary on their accounts.The aim of Magnusson’s study is to investigate the attitudes and practices of Australian and American healthcare workers towards assisted suicide and euthanasia, especially within HIV/AIDS healthcare contexts. While this presents some atypical features from other healthcare contexts where assisted death is an issue , it serves as a useful focal point for this study. The book presents and analyses first person accounts of involvement in …. (shrink)