Positive families and Boolean chains of copies of ultrahomogeneous structures

Miloš S. Kurilić; Boriša Kuzeljević

doi:10.5802/crmath.82

Logique mathématique

Positive families and Boolean chains of copies of ultrahomogeneous structures

Miloš S. Kurilić ¹ ; Boriša Kuzeljević ¹

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.

Résumé

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 $ℙ (𝕏) = {A \subset X : 𝔸 ≅ 𝕏}$ 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 $𝕃 ∖ {min 𝕃}$ in $〈ℙ (𝕏), \subset〉$ .

Reçu le : 2019-04-06
Révisé le : 2020-05-27
Accepté le : 2020-06-02
Publié le : 2020-11-16

DOI : 10.5802/crmath.82

Classification : 03C15, 03C50, 20M20, 06A06, 06A05

Affiliations des auteurs :

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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     author = {Milo\v{s} S. Kurili\'c and Bori\v{s}a Kuzeljevi\'c},
     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},
     number = {7},
     year = {2020},
     doi = {10.5802/crmath.82},
     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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