Some relations between k-analytic sets and generalized Borel sets

On Infinitary Rational Relations and Borel Sets

We prove in this paper that there exists some infinitary rational relations which are Σ03-complete Borel sets and some others which are Π03-complete. These results give additional answers to questions of Simonnet [Sim92] and of Lescow and Thomas [Tho90] [LT94].

Some points on generalized open sets

The paper is an attempt to represent a study of limit points, boundary points, exterior points, border, interior points and closure points in the common generalized topological space. This paper takes a look at the possibilities of an extended topological space and it also considers the new characterizations of dense set.

Generalized Rough Sets and Relations

In this paper, we introduce the notions of generalized upper (lower) approximations, generalized upper (lower) bounded operations and various operations. We investigate their properties. Mathematics Subject Classification: 03B52, 03B70, 03G25

Borel Sets and Countable Models

We show that certain families of sets and functions related to a countable structure A are analytic subsets of a Polish space. Examples include sets of automorphisms, endomorphisms and congruences of A and sets of the combinatorial nature such as coloring of countable plain graphs and domino tiling of the plane. This implies, without any additional set-theoretical assumptions, i.e., in ZFC alon...

A Course on Borel Sets