Comptes Rendus
no. 7
Logique mathématique
Positive families and Boolean chains of copies of ultrahomogeneous structures
Miloš S. Kurilić1 ; Boriša Kuzeljević1
1 Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad
Comptes Rendus. Mathématique, Volume 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
Miloš S. Kurilić 1 ; Boriša Kuzeljević 1

1 Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Positive families and {Boolean} chains of copies of ultrahomogeneous structures},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {791--796},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
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     year = {2020},
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     language = {en},
}
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Miloš S. Kurilić; Boriša Kuzeljević. Positive families and Boolean chains of copies of ultrahomogeneous structures. Comptes Rendus. Mathématique, Volume 358 (2020) no. 7, pp. 791-796. doi : 10.5802/crmath.82. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.82/

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