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We prove that the interval topology of an Archimedean atomic lattice effect algebra is Hausdorff whenever the set of all atoms of is almost orthogonal. In such a case is order continuous. If moreover is complete then order convergence of nets of elements of is topological and hence it coincides with convergence in the order topology and this topology is compact Hausdorff compatible with a uniformity induced by a separating function family on corresponding to compact and cocompact elements....
One of the possible models of fuzzification of non-transferable utility (NTU) coalitional games was extensively treated in [4]. In this paper, we suggest an alternative structure of fuzzification of the NTU games, where for every coalition a fuzzy class of (generally crisp) sets of its admissible pay-off vectors is considered. It is shown that this model of a fuzzy coalitional game can be represented by a fuzzy class of deterministic NTU games, and its basic concepts like the superadditivity or...
In this paper we sketch the development and give a model of the formal version of a generalization of the Alternative Set Theory.
We introduce the altitudes of a triangle (the cevians perpendicular to the opposite sides). Using the generalized Ceva’s Theorem, we prove the existence and uniqueness of the orthocenter of a triangle [7]. Finally, we formalize in Mizar [1] some formulas [2] to calculate distance using triangulation.
The purpose of this article is to connect the notion of the amenability of a discrete group with a new form of structural Ramsey theory. The Ramsey-theoretic reformulation of amenability constitutes a considerable weakening of the Følner criterion. As a by-product, it will be shown that in any non-amenable group G, there is a subset E of G such that no finitely additive probability measure on G measures all translates of E equally. The analysis of discrete groups will be generalized to the setting...
Moore [Fund. Math. 220 (2013)] characterizes the amenability of the automorphism groups of countable ultrahomogeneous structures by a Ramsey-type property. We extend this result to the automorphism groups of metric Fraïssé structures, which encompass all Polish groups. As an application, we prove that amenability is a condition.
In this paper we consider those Fraïssé classes which admit companion classes in the sense of [KPT]. We find a necessary and sufficient condition for the automorphism group of the Fraïssé limit to be amenable and apply it to prove the non-amenability of the automorphism groups of the directed graph S(3) and the boron tree structure T. Also, we provide a negative answer to the Unique Ergodicity-Generic Point problem of Angel-Kechris-Lyons [AKL]. By considering , where is the countably infinite-dimensional...
This paper has three parts. First, we study and characterize amenable and extremely amenable topological semigroups in terms of invariant measures using integral logic. We prove definability of some properties of a topological semigroup such as amenability and the fixed point on compacta property. Second, we define types and develop local stability in the framework of integral logic. For a stable formula ϕ, we prove definability of all complete ϕ-types over models and deduce from this the fundamental...
The ample hierarchy of geometries of stables theories is strict. We generalise the construction of the free pseudospace to higher dimensions and show that the n-dimensional free pseudospace is ω-stable n-ample yet not (n+1)-ample. In particular, the free pseudospace is not 3-ample. A thorough study of forking is conducted and an explicit description of canonical bases is given.
We give an abstract version of Sierpiński's theorem which says that the closure in the uniform convergence topology of the algebra spanned by the sums of lower and upper semicontinuous functions is the class of all Baire 1 functions. Later we show that a natural generalization of Sierpiński's result for the uniform closure of the space of all sums of A and CA functions is not true. Namely we show that the uniform closure of the space of all sums of A and CA functions is a proper subclass of the...
Hong and Do[4] improved Mareš[7] result about additive decomposition of fuzzy quantities concerning an equivalence relation. But there still exists an open question which is the limitation to fuzzy quantities on R (the set of real numbers) with bounded supports in the presented theory. In this paper we restrict ourselves to fuzzy numbers, which are fuzzy quantities of the real line R with convex, normalized and upper semicontinuous membership function and prove this open question.
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