We prove, in ZFC,the existence of a definable, countably saturated elementary extension of the reals.

We prove that in the Solovay model, every OD equivalence relation, E, over the reals, either admits an OD reduction to the equality relation on the set of all countable (of length $ ) binary sequences, or continuously embeds E 0 , the Vitali equivalence. If E is a Σ 1 1 (resp. Σ 1 2 ) relation then the reduction above can be chosen in the class of all ▵ 1 (resp. ▵ 2 ) functions. The proofs are based (...) on a topology generated by OD sets. (shrink)

Russian Orthodoxy during the twentieth century presented a rich and varied body of thought about the nature of humanity and the human condition. This article surveys the major thinkers within this tradition, beginning with its background in the Slavophile movement and culminating in the work of more recent Orthodox thinkers such as Sergei Bulgakov, Georges Florovsky, Vladimir Lossky, and Alexander Schmemann.

In this paper we summarise the constraints that low-redshift data—such as supernovae Ia, baryon acoustic oscillations and cosmic chronometers —are able to set on the concordance model and its extensions, as well as on inhomogeneous but isotropic models. We provide a broad overlook into these cosmological scenarios and several aspects of data analysis. In particular, we review a number of systematic issues of SN Ia analysis that include magnitude correction techniques, selection bias and their influence on the inferred cosmological constraints. (...) Furthermore, we examine the isotropic and anisotropic components of the BAO data and their individual relevance for cosmological model-fitting. We extend the discussion presented in earlier works regarding the inferred dynamics of cosmic expansion and its present rate from the low-redshift data. Specifically, we discuss the cosmological constraints on the accelerated expansion and related model-selections. In addition, we extensively talk about the Hubble constant problem, then focus on the low-redshift data constraint on \ that is based on CC. Finally, we present the way in which this result compares to the high-redshift \ estimate and local measurements that are in tension. (shrink)

The author examines the key philosophical problem of theodicy and freedom as it was first formulated by Fyodor Dostoevsky and later developed by Nikolai Berdyaev.

We consider games over a finite alphabet with Gurevich-Harrington's winning conditions and restraints as in Yakhnis-Yakhnis . The game tree, the Gurevich-Harrington's kernels of the winning condition and the restraints are defined by finite automata. We give an effective criterion to determine the winning player and an effective presentation of a class of finite automata defined winning strategies.Our approach yields an alternative solution to the games considered by Büchi and Landweber . The BL algorithm is an important tool for solving (...) effectively presented games. The differences between the BL and our algorithms are as follows. Our algorithm is uniformly applicable to winning sets that correspond to boolean combinations of BL winning conditions, while the BL algorithm requires a transformation of such boolean combinations into a single BL condition. Our algorithm directly applies to a larger class of game trees for a given game alphabet than does the BL one. We describe Büchi-Landweber's class of winning conditions in a more transparent way by using finite automata and Gurevich-Harrington's form of winning conditions. Our algorithms that determine the winner of the game and find a winning strategy, are based on a translation of the events in the game in terms of the transition table of the automaton representing the game. This automaton differs from the ones that represent BL winning conditions. Both algorithms need further investigation.The algorithm determining the winner in the game, can be used as a verifier of concurrent programs. This is because programs can be viewed as strategies in Gurevich-Harrington's games and program specifications could be regarded as winning conditions for such games. The algorithm which finds a winning strategy could be used as a basis for automated concurrent program design.The present paper is a sequel to Annals of Pure and Applied Logic 48 277–297. (shrink)

This study focuses on determining whether violent contexts influence the perception of aggressiveness in faces analysing spontaneous corrugator supercilii activity. Participants viewed pictures of...

As variants of the Christian tradition have emerged through the centuries they have given rise to distinct versions of Christian metaphysics with divergent cosmological commitments. In the early Church, the Cappodocian fathers constructed a theological framework which focuses on the “personal” nature of reality. The personal nature of reality is central not only to understanding key theological doctrines, such as the Trinity, but also the cosmos itself. This essay explores the Cappodocian conception of the cosmos as personal both in its (...) origin and as a medium for an interpersonal relationship between God and creatures. (shrink)

En el presente escrito se intentará mostrar algunos desafíos que el mundo contemporáneo pone a la educación bajo el influjo de la globalización, procesos que afectan muchos ámbitos del pensar y del actuar humano. Expone una serie de conceptualizaciones sobre dicho tema e invita al análisis serio de ese fenómeno por sus implicaciones sociales.

In “Elementa Juris Naturalis” (1671) G.W. Leibniz formulated the genius intuition about the fundamental unity of juridical and Aristotelian modalities. Interpreting and explicating this intuition by virtue of the deontic logic G.W. Wright arrived to the conclusion that the unity of modalities in question is not an equivalence relation but an analogy one. However a complement for G.W. Wright’s explication of the intuition of G.W. Leibniz was submitted. This complement was a two-valued algebra of formal-natural-law philosophy of juridical and Aristotelian (...) modalities as moral-legal evaluation-functions determined by one variable. In thepresent paper I submit a binary generalization of the mentioned unary complement. By virtue of this generalization some significant shortcomings of the complement in question are eliminated. The generalization deals with the modalities as moral-legal evaluation-functions determined by two variables. (shrink)

There is a hitherto not recognized possibility effectively to use computer-based scientific investigating, teaching and learning strategies and resources in history of philosophy. This is especially interesting for comparative scientific investigations in history of philosophy, for distance learning and teaching it. Effectively to apply modern computer technologies one has to have an adequate mathematical simulation of the sphere of application. Therefore the paper starts with submitting a mathematical simulation of metaphysics (in general). Then this mathematical machinery is applied to a (...) representative concrete example, namely, to the metaphysical system of Parmenides of Elea. By means of the method submitted in this paper (and by virtue of computer) a user himself can create (construct) an adequate digital simulation of some computable aspect of any specific philosophical system. Here the digital method of investigating the history of philosophy is exemplified by applying it to the metaphysical system of Parmenides. According to the hypothesis underlying the mentioned method, metaphysics is formal axiology. Hence algebra of metaphysics is algebra of formal axiology. Therefore metaphysics of Parmenides is represented below as a system of equations of the formal-axiology algebra. This system of equations could be computer-generated and investigated by any user autonomously. (shrink)

We consider QED processes in the presence of an infinitely thin and infinitely long straight string with a magnetic flux inside it. The bremsstrahlung from an electron passing by the magnetic string and the electron-positron pair production by a single photon are reviewed. Based on the exact electron and positron solutions of the Dirac equation in the external Aharonov-Bohm potential we present matrix elements for these processes. The dependence of the resulting cross sections on energies, directions, and polarizations of the (...) involved particles is discussed for low energies. (shrink)

This article discusses the connection between the ideas of Fyodor M. Dostoevsky and Vladimir S. Solovyov on the need for cultural and moral transformation of those who would claim to participate in...

Recently, psychologists have explored moral concepts including obligation, blame, and ability. While little empirical work has studied the relationships among these concepts, philosophers have widely assumed such a relationship in the principle that “ought” implies “can,” which states that if someone ought to do something, then they must be able to do it. The cognitive underpinnings of these concepts are tested in the three experiments reported here. In Experiment 1, most participants judge that an agent ought to keep a promise (...) that he is unable to keep, but only when he is to blame for the inability. Experiment 2 shows that such “ought” judgments correlate with judgments of blame, rather than with judgments of the agent’s ability. Experiment 3 replicates these findings for moral “ought” judgments and finds that they do not hold for nonmoral “ought” judgments, such as what someone ought to do to fulfill their desires. These results together show that folk moral judgments do not conform to a widely assumed philosophical principle that “ought” implies “can.” Instead, judgments of blame play a modulatory role in some judgments of obligation. (shrink)