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

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
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     author = {\v{Z}arko Mijajlovi\'c and Dragan Doder and Angelina Ili\'c-Stepi\'c},
     title = {Borel {Sets} and {Countable} {Models}},
     journal = {Publications de l'Institut Math\'ematique},
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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/