Publications de l'Institut Mathématique, Nouvelle SérieVol. 90(105), pp. 1–11 (2011)
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Publications de l'Institut Mathématique, Nouvelle Série Vol. 90(105), pp. 1–11 (2011) |
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BOREL SETS AND COUNTABLE MODELSZarko Mijajlovic, Dragan Doder and Angelina Ilic-StepicUniversity 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 set-theoretical 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.
© 2011 Mathematical Institute of the Serbian Academy of Science and Arts
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