no. 7
Logique mathématique
Positive families and Boolean chains of copies of ultrahomogeneous structures
Kurilić, Miloš S.1 ; Kuzeljević, Boriša1
1 Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad
Comptes Rendus. Mathématique, Tome 358 (2020) no. 7, pp. 791-796.

A family of infinite subsets of a countable set X is called positive iff it is closed under supersets and finite changes and contains a co-infinite set. We show that a countable ultrahomogeneous relational structure 𝕏 has the strong amalgamation property iff the set ℙ(𝕏)={A⊂X:𝔸≅𝕏} contains a positive family. In that case the family of large copies of 𝕏 (i.e. copies having infinite intersection with each orbit) is the largest positive family in ℙ(𝕏), and for each ℝ-embeddable Boolean linear order 𝕃 whose minimum is non-isolated there is a maximal chain isomorphic to 𝕃∖{min𝕃} in ℙ(𝕏),⊂.

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DOI : 10.5802/crmath.82
Classification : 03C15, 03C50, 20M20, 06A06, 06A05
Kurilić, Miloš S. 1 ; Kuzeljević, Boriša 1

1 Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad 
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Kurilić, Miloš S.; Kuzeljević, Boriša. Positive families and Boolean chains of copies of ultrahomogeneous structures. Comptes Rendus. Mathématique, Tome 358 (2020) no. 7, pp. 791-796. doi : 10.5802/crmath.82. http://www.numdam.org/articles/10.5802/crmath.82/

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