Geodesic
Borel Sets and Countable Models
Publications de l'Institut Mathématique, _N_S_90 (2011) no. 104, p. 1

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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 : 03C07 
Žarko Mijajlović; Dragan Doder; Angelina Ilić-Stepić. Borel Sets and Countable Models. Publications de l'Institut Mathématique, _N_S_90 (2011) no. 104, p. 1 . http://geodesic.mathdoc.fr/item/PIM_2011_N_S_90_104_a0/
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     title = {Borel {Sets} and {Countable} {Models}},
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