| Autor: |
Kurilić, Miloš S., Kuzeljević, Boriša |
| Jazyk: |
English<br />French |
| Rok vydání: |
2020 |
| Předmět: |
|
| Zdroj: |
Comptes Rendus. Mathématique, Vol 358, Iss 7, Pp 791-796 (2020) |
| Druh dokumentu: |
article |
| ISSN: |
1778-3569 |
| DOI: |
10.5802/crmath.82 |
| Popis: |
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 ${\mathbb{X}}$ has the strong amalgamation property iff the set ${\mathbb{P}}({\mathbb{X}})\!=\! \lbrace A\!\subset \! X:{\mathbb{A}}\!\cong \!{\mathbb{X}}\rbrace $ contains a positive family. In that case the family of large copies of ${\mathbb{X}}$ (i.e. copies having infinite intersection with each orbit) is the largest positive family in ${\mathbb{P}}({\mathbb{X}})$, and for each ${\mathbb{R}}$-embeddable Boolean linear order ${\mathbb{L}}$ whose minimum is non-isolated there is a maximal chain isomorphic to ${\mathbb{L}}\setminus \lbrace \min {\mathbb{L}}\rbrace $ in $\left\langle {\mathbb{P}}({\mathbb{X}}),\subset \right\rangle $. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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