Cohesive powersof computable structures are effective analogs of ultrapowers, where cohesive sets play the role of ultrafilters. Let$\omega $,$\zeta $, and$\eta $denote the respective order-types of the natural numbers, the integers, and the rationals when thought of as linear orders. We investigate the cohesive powers of computable linear orders, with special emphasis on computable copies of$\omega $. If$\mathcal {L}$is a computable copy of$\omega $that is computably isomorphic to the usual presentation of$\omega $, then every cohesive power of$\mathcal {L}$has order-type$\omega + (...) \zeta \eta $. However, there are computable copies of$\omega $, necessarily not computably isomorphic to the usual presentation, having cohesive powers not elementarily equivalent to$\omega + \zeta \eta $. For example, we show that there is a computable copy of$\omega $with a cohesive power of order-type$\omega + \eta $. Our most general result is that if$X \subseteq \mathbb {N} \setminus \{0\}$is a Boolean combination of$\Sigma _2$sets, thought of as a set of finite order-types, then there is a computable copy of$\omega $with a cohesive power of order-type$\omega + \boldsymbol {\sigma }(X \cup \{\omega + \zeta \eta + \omega ^*\})$, where$\boldsymbol {\sigma }(X \cup \{\omega + \zeta \eta + \omega ^*\})$denotes the shuffle of the order-types inXand the order-type$\omega + \zeta \eta + \omega ^*$. Furthermore, ifXis finite and non-empty, then there is a computable copy of$\omega $with a cohesive power of order-type$\omega + \boldsymbol {\sigma }(X)$. (shrink)

Upon introspection, we judge that suffering feels bad. I argue there is no appearance-reality gap when it comes to introspective judgments about simple, intrinsic, nonrepresentational phenomenal states like itches, tingling, and suffering's feeling bad. On constitutivism about phenomenal introspection, there is no appearance-reality gap here because these judgments are literally constituted by the phenomenal states they are about. As a result, we are directly acquainted with the intrinsic properties of experience in having these judgments. Reflecting on our direct acquaintance with (...) intrinsic badness, we can know that our suffering instantiates this judgment-independent evaluative property. (shrink)

Let I be a quasimaximal subset of a computable basis of the fully efective vector space V ∞ . We give a necessary and sufficient condition for the existence of an isomorphism between the principal filter respectivelly. We construct both quasimaximal sets that satisfy and quasimaximal sets that do not satisfy this condition. With the latter we obtain a negative answer to Question 5.4 posed by Downey and Remmel in [3].

We construct a computable vector space with the trivial computable automorphism group, but with the dependence relations as complicated as possible, measured by their Turing degrees. As a corollary, we answer a question asked by A.S. Morozov in [Rigid constructive modules, Algebra and Logic, 28 570–583 ; 379–387 ].

Human beings differ in ways of understanding, interpreting, describing or sharing experience. On the basis of experience we construct our own conceptual systems (beliefs and values) that are neither consistent nor monolithic. "Alternative conceptual systems exist, whether one likes it or not. They are not likely to go away, since they arise from a fundamental human capacity to conceptualise experience...A refusal to recognise conceptual relativism where it exists does have ethical consequences. It leads directly to conceptual elitism and imperialism - (...) to the assumption that our behaviour is rational and that of other people is not, and to attempts to impose our way of thinking on others" (Lakoff, 1987; p.337). (shrink)

This article suggests an explorative approach to the character and meaning of individual autonomy in higher education through a particular conception of social relations. Following Axel Honneth, a theoretical framework is outlined in which subjectivity and autonomy are results of underlying institutionalised relations of recognition in the forms of love, legal respect, and social esteem. It is argued that when higher education is seen as self-formation and as a field of relations of recognition due to its collegial, legal, and evaluative (...) features, it is possible to conceive of its institutional environment as supportive or obstructive to recognition and, consequently, to the advancement of individual autonomy. Such a theoretical tool, based on Honneth’s recognition theory, could then translate into a critical instrument able to extend the understanding of what constitutes matters of individual autonomy in and across specific institutionalised contexts, including higher education. (shrink)

When encountering a set of alternatives displayed in the form of a list, the decision maker usually determines a particular alternative, after which she stops checking the remaining ones, and chooses an alternative from those observed so far. We present a framework in which both decision problems are explicitly modeled, and axiomatically characterize a ‘divide-and-choose’ rule which unifies successive choice and satisficing choice.

The ancient mythology could serve as an effective medium for metaphorically conveying complex concepts and principles to a broad spectrum of people. In this paper we show how the fuzzy logic approach can be used to translate the metaphoric language of ancient myths and legends into a 'soft' scientific paradigm which helps us to understand better the social complexity of our time.

According to leading Kant scholars, in mid-1760s Kant realizes that his program for the reform of metaphysics cannot be developed by the method of conceptual analysis which he had previously considered to be more adequate than the synthetic method of the Wolffians that imitates the mathematical one. In this paper, I put into question the claim of a pre-Critical project of ‘analytical metaphysics’ by trying to show that even for the ‘pre-Critical’ Kant the proper method of metaphysics is genuinely synthetic, (...) but the synthetic construction in question should have been prepared by a Critical and subsequent exhaustive analysis of key material-instrumental concepts of the peculiar philosophical science under question. (shrink)

Review on Vaclav Nemec, Marius Victorinus: The Consubstantiality of The Trinity OIKOYMENH, Prague, 2006.

Let I0 be a a computable basis of the fully effective vector space V∞ over the computable field F. Let I be a quasimaximal subset of I0 that is the intersection of n maximal subsets of the same 1-degree up to *. We prove that the principal filter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{L}^{\ast}(V,\uparrow )}$$\end{document} of V = cl(I) is isomorphic to the lattice \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{L}(n, \overline{F})}$$\end{document} of subspaces (...) of an n-dimensional space over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{F}}$$\end{document}, a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma _{3}^{0}}$$\end{document} extension of F. As a corollary of this and the main result of Dimitrov (Math Log 43:415–424, 2004) we prove that any finite product of the lattices \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(\mathcal{L}(n_{i}, \overline{F }_{i}))_{i=1}^{k}}$$\end{document} is isomorphic to a principal filter of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{ L}^{\ast}(V_{\infty})}$$\end{document}. We thus answer Question 5.3 “What are the principal filters of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{L}^{\ast}(V_{\infty})?}$$\end{document} ” posed by Downey and Remmel (Computable algebras and closure systems: coding properties, handbook of recursive mathematics, vol 2, pp 977–1039, Stud Log Found Math, vol 139, North-Holland, Amsterdam, 1998) for spaces that are closures of quasimaximal sets. (shrink)

Humanity and water represent an intersection of two natural cycles: the human economy and the earth's hydrological system. Although water is vital for human survival and growth, the point where human endeavor intersects is the most variable and uncertain in the hydrological system. Significant spatial and temporal variation of evaporation and rainfall has led to a number of responses aimed at increasing certainty of access to water. However, many of the world's civilizations can attest that the very act of reducing (...) water uncertainty by technical means (capture, storage, and irrigation) has ultimately led to greater uncertainty and civilization failure. This article explores the concept of living with water as a complex entity, inseparably connected with all three levels of existential complexity - individual, social, and ecological - rather than as a commodity, which has led to our current uncertain status. (shrink)

Optimal shelflisting invites profit maximization to become sensitive to the ways in which purchasing decisions are order-dependent. We study the computational complexity of the corresponding product arrangement problem when consumers are either rational maximizers, use a satisficing procedure, or apply successive choice. The complexity results we report are shown to crucially depend on the size of the top cycle in consumers’ preferences over products and on the direction in which alternatives on the shelf are encountered.

We present a unified look at myopic stability concepts for hedonic games, and discuss the status of the existence problems of stable coalition structures. In particular, we show that contractual strictly core stable coalition structures always exist, and present a sufficient condition for the existence of contractually Nash stable coalition structures on the class of separable games.

Resumen: El artículo está dedicado a Vladimir Solovyov (Vladimir Solovyov) (1853-1900), el filósofo religioso más grande de Rusia del siglo 19. La tesis fundamental es que las ideas principales de Solovyov se pueden interpretar como una reflexión filosófica sobre los sentimientos religiosos fundamentales y los aspectos de comportamiento religioso. En este sentido se analizan en detalle las enseñanzas de Solovyov sobre la unidad positiva (all-encompassing unity, всеединство), la catolicidad (sobornost, соборность) y la divinohumanidad (Godmanhood, Divine Humanity, богочеловечество). Se presta atención (...) especial al proyecto teocrático de Solovyov de establecer una Iglesia Cristiana Universal (Christian Universal Church, Ecumenical Church) y restaurar la unidad (re-unification) de la cristiandad.Palabras clave:unidad, divinohumanidad; catolicidad; ortodoxia rusa (Russian Orthodoxy); Iglesia Universal (Ecumenical Church; Universal Church). (shrink)