We give a classification of all the countable homogeneous multipartite graphs. This generalizes the similar result for bipartite graphs given in [5]. 2010 Mathematics Subject Classification 05C99 keywords: multipartite graph, homogeneous, classification

Introduction, Let © be the class of all countable and connected perfectly separable Hausdorff spaces containing more than one point. I t is known that an ©-space cannot be regular or compact. Urysohn, using a complicated identification of points, has constructed the first example of an ©-space. Two ©-spaces, X and X*, more simply constructed and not involving identifications, are presented here...

This is a revised and extended version of an article which encapsulates a key aspect of the “Henkin method” in a general result about the existence of finitely consistent theories satisfying prescribed closure conditions. This principle can be used to give streamlined proofs of completeness for logical systems, in which inductive Henkin-style constructions are replaced by a demonstration that a...

Region Connection Calculus (RCC) is the most widely studied formalism of Qualitative Spatial Reasoning. It has been known for some time that each connected regular topological space provides an RCC model. These ‘standard’ models are inevitable uncountable and regions there cannot be represented finitely. This paper, however, draws researchers’ attention to RCC models that can be constructed fro...

A space X is called an α-Toronto space if X is scattered of Cantor– Bendixson rank α and is homeomorphic to each of its subspaces of the same rank. We answer a question of Steprāns by constructing a countable α-Toronto space for each α ≤ ω. We also construct consistent examples of countable α-Toronto spaces for each

The computability of countable subshifts and their members is examined. Results include the following. Subshifts of CantorBendixson rank one contain only eventually periodic elements. Any rank one subshift, in which every limit point is periodic, is decidable. Subshifts of rank two may contain members of arbitrary Turing degree. In contrast, effectively closed (Π 1 ) subshifts of rank two conta...

Let {Σα}α<ω1 , where ω1 is the first non-countable ordinal, denote the Borel hierarchy of subsets of the Cantor space 2. As usual, Πα denotes the dual class for Σα while ∆ 0 α = Σ 0 α ∩Πα — the corresponding ambiguous class. Let B = ∪α<ω1Σα denote the class of all Borel sets. The levels of Borel hierarchy, as well as many other classes of interest for descriptive set theory, may be defined by m...

Two countable lters on ! are incompatible if they have no common innnite pseudo-intersection. Letting a(P f) denote the minimal size of a maximal uncountable family of pairwise incompatible countable lters on !, we prove the consistency of t < a(P f).

We consider countable Borel equivalence relations on quotient Borel spaces. We prove a generalization of the representation theorem of Feldman–Moore, but provide some examples showing that other very simple properties of countable equivalence relations on standard Borel spaces may fail in the context of nonsmooth quotients. In this paper we try to analyze some very basic questions about the str...

Many authors have proposed fixed-point algorithms for obtaining a fixed point of G-nonexpansive mappings without using inertial techniques. To improve convergence behavior, some accelerated methods been introduced. The main aim this paper is to use coordinate affine structure create an algorithm with technique countable family in Hilbert space symmetric directed graph G and prove the weak theor...