Authors: Mijajlović, Žarko
Doder, Dragan
Ilić Stepić, Angelina 
Title: Borel sets and countable models
Journal: Publications de l'Institut Mathematique
Volume: 90
Issue: 104
First page: 1
Last page: 11
Issue Date: 1-Dec-2011
Rank: M24
ISSN: 0350-1302
DOI: 10.2298/PIM1104001M
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 alone, that cardinality of every such uncountable set is 2 א0.
Publisher: Mathematical Institute of the SASA
Project: Representations of logical structures and formal languages and their application in computing 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 

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