Publications de l'Institut Mathématique, Nouvelle Série Vol. 90(105), pp. 1–11 (2011) 

BOREL SETS AND COUNTABLE MODELSZarko Mijajlovic, Dragan Doder and Angelina IlicStepicUniversity of Belgrade, Faculty of Mathematics, Belgrade, Serbia and University of Belgrade, Faculty of Mechanical Engineering, Belgrade, SerbiaAbstract: We show that certain families of sets and functions related to a countable structure $\Bbb{A}$ are analytic subsets of a Polish space. Examples include sets of automorphisms, endomorphisms and congruences of $\Bbb{A}$ and sets of the combinatorial nature such as coloring of countable plain graphs and domino tiling of the plane. This implies, without any additional settheoretical assumptions, i.e., in ZFC alone, that cardinality of every such uncountable set is $2^{\aleph_0}$. Classification (MSC2000): 03C07 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 16 Nov 2011. This page was last modified: 30 Nov 2011.
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