Towards a Ryll-Nardzewski-type theorem for weakly oligomorphic structures
| Autor: | Maja Pech, Christian Pech |
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| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Property (philosophy) 010102 general mathematics Structure (category theory) 0102 computer and information sciences Type (model theory) Characterization (mathematics) 16. Peace & justice 01 natural sciences Mathematics::Logic 010201 computation theory & mathematics Core (graph theory) Countable set Homomorphism Isomorphism 0101 mathematics Mathematics |
| Zdroj: | Mathematical Logic Quarterly. 62:25-34 |
| ISSN: | 0942-5616 |
| DOI: | 10.1002/malq.201400067 |
| Popis: | A structure is called weakly oligomorphic if it realizes only finitely many n-ary positive existential types for every n. The goal of this paper is to show that the notions of homomorphism-homogeneity, and weak oligomorphy are not only completely analogous to the classical notions of ultrahomogeneity and oligomorphy, but are actually closely related. A first result is a Fra¨osse-type theorem for homomorphism-homogeneous relational structures. Further we show that every weakly oligomorphic homomorphism-homogeneous structure contains (up to isomorphism) a unique homogeneous, homomorphism- homogeneous core, to which it is homomorphism-equivalent. As a consequence, we obtain that every countable weakly oligomorphic structure is homomorphism- equivalent with a finite or !-categorical structure. Another result is the characterization of positive existential theories of weakly oligomorphic structures as the positive existential parts of !-categorical theories. Finally, we show, that the countable models of countable weakly oligomorphic structures are mutually homomorphism-equivalent (we call first order theories with this property weakly !-categorical). These results are in analogy with part of the Engeler-Ryll-Nardzewski-Svenonius-theorem. |
| Databáze: | OpenAIRE |
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