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||Abstract:||
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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