LetMbe a countably infinite ω-categorical structure. Consider Aut(M) as a complete metric space by definingd(g, h) = Ω{2−n:g(xn) ≠h(xn) org−1(xn) ≠h−1(xn)} where {xn:n∈ ω} is an enumeration ofMAn automorphism α ∈ Aut(M) is generic if its conjugacy class is comeagre. J. Truss has shown in [11] that if the set P of all finite partial isomorphisms contains a co-final subset P1closed under conjugacy and having the amalgamation property and the joint embedding property then there is a generic automorphism. In the (...) present paper we give a weaker condition of this kind which is equivalent to the existence of generic automorphisms. Really we give more: a characterization of the existence of generic expansions (defined in an appropriate way) of an ω-categorical structure. We also show that Truss' condition guarantees the existence of a countable structure consisting of automorphisms ofMwhich can be considered as an atomic model of some theory naturally associated toM. We do it in a general context of weak models for second-order quantifiers.The author thanks Ludomir Newelski for pointing out a mistake in the first version of Theorem 1.2 and for interesting discussions. Also, the author is grateful to the referee for very helpful remarks. (shrink)

The notion of a strongly determined type over A extending p is introduced, where p .S. A strongly determined extension of p over A assigns, for any model M )- A, a type q S extending p such that, if realises q, then any elementary partial map M → M which fixes acleq pointwise is elementary over . This gives a crude notion of independence which arises very frequently. Examples are provided of many different kinds of theories with strongly determined (...) types, and some without. We investigate a notion of multiplicity for strongly determined types with applications to ‘involved’ finite simple groups, and an analogue of the Finite Equivalence Relation Theorem. Lifting of strongly determined types to covers of a structure is discussed, and an application to finite covers is given. (shrink)

We give an example of a simple ω-categorical theory such that for any finite set of parameters the corresponding constant expansion does not satisfy the PAPA. We describe a wide class of homogeneous structures with generic automorphisms and show that some natural reducts of our example belong to this class.

The paper is devoted to Nikolay Lossky who was one of the leading Russian philosophers of the first half of the twentieth century. We demonstrate the interrelationship between three aspects of Lossky’s philosophy: realism in the theory of knowledge, hierarchical personalism, and supra-naturalistic concept of evolution. We pay attention to the contemporary relevance of Lossky, and we discuss and critique his ideas in light of those of other philosophers. Lossky acknowledges that the subject interacts with being itself and that knowledge (...) is not a shadow or copy of being. His ontology is based on intuitivism and epistemological optimism. Its main categories are God, as the super-systematic principle, and monads. In Lossky’s metaphysics, the idea of abstract ideal principles of being is quite harmoniously combined with personalism. Lossky’s ontology has strong ethical underpinnings. He considers that values are rooted in being and that the evolution of the world is directed by God towards the good. Lossky elaborates a supra-naturalistic concept of evolution. He extrapolates principles of teleological determination, which are fundamental to human existence, on the underlying levels of the world as a whole. Many trends of modern thought are in tune with Lossky’s philosophy, including a return to metaphysics, panpsychism, Platonism, and the desire to unite the religious worldview with new scientific discoveries. (shrink)

The age of a structure M is the set of all isomorphism types of finite substructures of M. We study ages of generic expansions of ω-stable ω-categorical structures.

The main result of the paper states that there is a finitely presented group _G_ with decidable word problem where detection of finite subsets of _G_ which generate amenable subgroups is not decidable.

Este artigo busca expor as críticas de Bernardo de Claraval às superfluidades humanas no texto da Apologia, especialmente aquelas referentes à arte arquitetural. Em segundo lugar, procura analisar as implicações estéticas do ascetismo cisterciense e bernardiano. As críticas de Bernardo exercem uma influência decisiva na ornamentação e fazem nascer uma nova arquitetura. This paper is to expose the criticism of human superfluities at Bernard of Clairvaux in the text of the Apology, especially those related to architectural art. Secondly, analyzes the (...) aesthetic implications of cistercian and bernardian asceticism. Criticism of Bernard exercise a decisive influence on ornamentation and give birth to a new architecture. (shrink)

We study the situation when the automorphism group of a recursively saturated structure acts on an ℝ-tree. The cases of and models of Peano Arithmetic are central in the paper.

It is shown that for every Turing degree d there is an ω-categorical group G such that the isomorphism type of G is of degree d. We also find an ω-categorical group G such that the isomorphism type of G has no degree.

Este artigo busca expor as críticas de Bernardo de Claraval às superfluidades humanas no texto da Apologia , especialmente aquelas referentes à arte arquitetural. Em segundo lugar, procura analisar as implicações estéticas do ascetismo cisterciense e bernardiano. As críticas de Bernardo exercem uma influência decisiva na ornamentação e fazem nascer uma nova arquitetura.

We show that for every sofic chunk E there is a bijective homomorphism \, where \ is a chunk of the group of computable permutations of \ so that the approximating morphisms of E can be viewed as restrictions of permutations of \ to finite subsets of \. Using this we study some relevant effectivity conditions associated with sofic chunks and their profiles.

In this article we examine the main fragments of Thomas Aquinas regarding beauty. Our approach allows us to acquire the repertoire of definitions of beauty that are found in his commentaries and thought. Thus our scope is reconstruct at the theory of beauty that is implicit in Thomas Aquinas.

We study complexity of the index set of countably categorical theories and Ehrenfeucht theories in finite languages.

We are a Sophiic people, we are subjects of Sophia and must be chivalrously loyal to our queen. That is the guarantee of our existence, for "Russia" and "Russian" without Sophia is a contradiction.

We study expressive power of continuous logic in classes of metric groups defined by properties of their actions. We concentrate on unbounded continuous actions on metric spaces. For example, we consider the properties non‐OB, non‐FH and non‐FR.