| Autor: |
B. Sh. Kulpeshov, S. V. Sudoplatov |
| Rok vydání: |
2023 |
| Zdroj: |
Herald of the Kazakh-British technical university. 20:6-13 |
| ISSN: |
1998-6688 |
| DOI: |
10.55452/1998-6688-2023-20-1-6-13 |
| Popis: |
The present paper concerns the notion of weak o-minimality introduced by M. Dickmann and originally deeply studied by D. Macpherson, D. Marker, and C. Steinhorn. Weak o-minimality is a generalization of the notion of o-minimality introduced by A. Pillay and C. Steinhorn in series of joint papers. As is known, the ordered field of real numbers is an example of an o-minimal structure. We continue studying model-theoretic properties of o-minimal and weakly o-minimal structures. In particular, we introduce the notion of almost 1-transitivity in linearly ordered structures and study tits properties. Almost 1-transitive o-minimal and weakly o-minimal linear orderings have been described. It has been established that an almost 1-transitive weakly o-minimal linear ordering is isomorphic to a finite number of concatenations of almost 1-transitive o-minimal linear orderings. Properties of expansions of families of almost 1-transitive linearly ordered theories are studied. Rank values for families of almost 1-transitive o-minimal and weakly o-minimal linear orderings have been found. A criterion for preserving both the almost 1-transitivity and weak o-minimality has been found at expanding an almost 1-transitive weak o-minimal theory by an arbitrary unary predicate. Dense ordering of an almost 1-transitive weakly o-minimal theory that is almost omega-categorical has been established. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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