In this paper, the notions of Fα-categorical and Gα-categorical structures are introduced by choosing the isomorphism such that the function itself or its graph sits on the α-th level of the Ershov hierarchy, respectively. Separations obtained by natural graphs which are the disjoint unions of countably many finite graphs. Furthermore, for size-bounded graphs, an easy criterion is given to say when it is computable-categorical and when it is only G2-categorical; in the latter case it is not Fα-categorical for any (...) recursive ordinal α. (shrink)

Includes bibliographical references and index.

An Ax-Kochen-Ershov principle for intermediate structures between valued groups and valued fields. We will consider structures that we call valued B-groups and which are of the form $\langle G, B, *, v\rangle$ where - G is an abelian group, - B is an ordered group, - v is a valuation defined on G taking its values in B, - * is an action of B on G satisfying: ∀ x ∈ G ∀ b ∈ B v(x * b) = (...) v(x) · b. The analysis of Kaplanski for valued fields can be adapted to our context and allows us to formulate an Ax-Kochen-Ershov principle for valued B-groups: we axiomatise those which are in some sense existentially closed and also obtain many of their model-theoretical properties. Let us mention some applications: 1. Assume that v(x) = v(nx) for every integer n ≠ 0 and x ∈ G, B is solvable and acts on G in such a way that, for the induced action, $\mathbb{Z}[B] \setminus \{0\}$ embeds in the automorphism group of G. Then $\langle G, B, *, v\rangle$ is decidable if and only if B is decidable as an ordered group. 2. Given a field k and an ordered group B, we consider the generalised power series field k((B)) endowed with its canonical valuation. We consider also the following structure: $\mathbf{M} = \langle k((B))_+, S, v, \times \upharpoonright_{k((B))\times S}\rangle,$ where k((B)) + is the additive group of k((B)), S is a unary predicate interpreting ${T^b| b \in B}$ , and $\times \upharpoonright_{k((B))\times S}$ is the multiplication restricted to k((B))× S, structure which is a reduct of the valued field k((B)) with its canonical cross section. Then our result implies that if B is solvable and decidable as an ordered group, then M is decidable. 3. A valued B-group has a residual group and our Ax-Kochen-Ershov principle remains valid in the context of expansions of residual group and value group. In particular, by adding a residual order we obtain new examples of solvable ordered groups having a decidable theory. (shrink)

The nature of Marx's ethics has been a matter of considerable dispute since the latter part of the nineteenth century. Some have maintained that Marx had no ethics; others have claimed that his ethics is Kantian; and yet others have maintained that his ethics is utilitarian. The first two views were prominent at the turn of the century. It is the utilitarian view that seems to hold favor among a great many today. Thus Adam Schaff has claimed that ‘Marxist theory (...) … leads to the general position that may be called “social hedonism” —the view that the aim of human life is to secure the maximum happiness for the broadest masses of the people … ’ Similarly, Derek Allen has claimed that ‘it is possible … to show that the arguments which support [Marx's and Engels’] moral judgments are utilitarian in all but name.’. (shrink)

The nature of Marx's ethics has been a matter of considerable dispute since the latter part of the nineteenth century. Some have maintained that Marx had no ethics; others have claimed that his ethics is Kantian; and yet others have maintained that his ethics is utilitarian. The first two views were prominent at the turn of the century. It is the utilitarian view that seems to hold favor among a great many today. Thus Adam Schaff has claimed that ‘Marxist theory (...) … leads to the general position that may be called “social hedonism” —the view that the aim of human life is to secure the maximum happiness for the broadest masses of the people … ’ Similarly, Derek Allen has claimed that ‘it is possible … to show that the arguments which support [Marx's and Engels’] moral judgments are utilitarian in all but name.’. (shrink)

This book addresses a wide range of topics relating to the properties and behavior of condensed matter under extreme conditions such as intense magnetic and electric fields, high pressures, heat and cold, and mechanical stresses. It is divided into four sections devoted to condensed matter theory, molecular chemistry, theoretical physics, and the philosophy and history of science. The main themes include electronic correlations in material systems under extreme pressure and temperature conditions, surface physics, the transport properties of low-dimensional electronic systems, (...) applications of the density functional theory in molecular systems, and graphene. The book is the outcome of a workshop held at the University of Catania, Italy, in honor of Professor Renato Pucci on the occasion of his 70th birthday. It includes selected invited contributions from collaborators and co-authors of Professor Pucci during his long and successful career, as well as from other distinguished guest authors. (shrink)

Lachlan observed that any nonzero d.c.e. degree bounds a nonzero c.e. degree. In this paper, we study the c.e. predecessors of d.c.e. degrees, and prove that given a nonzero d.c.e. degree , there is a c.e. degree below and a high d.c.e. degree such that bounds all the c.e. degrees below . This result gives a unified approach to some seemingly unrelated results. In particular, it has the following two known theorems as corollaries: there is a low c.e. degree isolating (...) a high d.c.e. degree [S. Ishmukhametov, G. Wu, Isolation and the high/low hierarchy, Arch. Math. Logic 41 259–266]; there is a high d.c.e. degree bounding no minimal pairs [C.T. Chong, A. Li, Y. Yang, The existence of high nonbounding degrees in the difference hierarchy, Ann. Pure Appl. Logic 138 31–51]. (shrink)

The AGI alignment problem has a bimodal distribution of outcomes with most outcomes clustering around the poles of total success and existential, catastrophic failure. Consequently, attempts to solve AGI alignment should, all else equal, prefer false negatives (ignoring research programs that would have been successful) to false positives (pursuing research programs that will unexpectedly fail). Thus, we propose adopting a policy of responding to points of philosophical and practical uncertainty associated with the alignment problem by limiting and choosing necessary assumptions (...) to reduce the risk of false positives. Herein we explore in detail two relevant points of uncertainty that AGI alignment research hinges on---meta-ethical uncertainty and uncertainty about mental phenomena---and show how to reduce false positives in response to them. (shrink)

The theoretical and practical problems of providing incentives for people's activity in society are becoming increasingly more urgent as the role of the human factor in the development of society grows. In light of modern historical experience, we can see the onesidedness of conceptions according to which the types and directions of activity are mechanically predetermined by conditions external to it, and we can see the necessity of understanding the laws of activity itself in all their complicated dialectical essence. These (...) problems have become particularly important at the present stage of development of Soviet society, when a greater active involvement of the masses and profound changes in social psychology are becoming acutely necessary. (shrink)

v. 1. Recursive model theory -- v. 2. Recursive algebra, analysis and combinatorics.

(1996). The notion of citizenship in France and its redefinition. The European Legacy: Vol. 1, Fourth International Conference of the International Society for the study of European Ideas, pp. 575-579.

system reflected in Saussure's linguistic theory, and so influential in the great progress linguistic theory has made in this century. Indeed, Granger sees linguistic theory as expressing a paradigm for scientific theorizing, which research in other social sciences should adopt. But 'structuralism' as a method in science does not, in Granger's view, begin with Saussure and the linguists. It is nothing less than the strategy of all the sciences, both natural and social, since their beginnings. Now, 'structuralism' is a 'trendy' (...) term no less in Anglophone methodology than in Francophone philosophy. But Granger's employment of the term is not to be assimilated to this trend, nor to the fashionable excesses for which this expression has been a watch word (he explicitly separates himself from this movement in the preface to the second edition). The exact nature of what Granger calls 'structuralist' methods is the subject of a large part of this work, and I will not dwell on it much further in this introduction. Suffice it to say that Granger's demand for structuralist description is nothing less than the recognition that the successful pursuit of science requires that its terms and predicates pick out what we may call 'natural kinds'; that is, describe classes of items that bear uniform nomolog ical relations to one another. A science whose descriptive terms do not meet this condition will never produce any laws that reflect such nomological connections. (shrink)