Remarks on weak o-minimality
| dc.contributor.author | Kudaibergenov K. Zh. | |
| dc.date.accessioned | 2025-11-19T05:03:59Z | |
| dc.date.available | 2025-11-19T05:03:59Z | |
| dc.date.issued | 2008 | |
| dc.description.abstract | This paper investigates several necessary and sufficient conditions for weak o-minimality in expansions of linearly ordered structures. Building on earlier results, we provide a simplified proof of the main theorem of Kulpeshov, which characterizes weak o-minimality in terms of convexity of realizations of types. Additionally, two further equivalent conditions for weak o-minimality are established, involving types containing cuts and convexity properties of definable sets. A new, more conceptual proof of Pillay and Steinhorn’s characterization of full o-minimality is also presented. Furthermore, we examine weakly o-minimal ordered rings and show that every weakly o-minimal Archimedean ordered ring is necessarily a real closed field. This result follows from structural properties of definable subgroups in weakly o-minimal groups and known criteria for ordered fields. Overall, the paper clarifies foundational connections between weak o-minimality, type spaces, and definable order structures. | |
| dc.identifier.citation | Kudaibergenov K. Zh. / Remarks on weak o-minimality / Suleyman Demirel University / Сду хабаршысы, 2008 | |
| dc.identifier.uri | https://repository.sdu.edu.kz/handle/123456789/2215 | |
| dc.language.iso | en | |
| dc.publisher | Suleyman Demirel University | |
| dc.rights | Attribution-NonCommercial-ShareAlike 4.0 International | en |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | |
| dc.subject | weak o-minimality | |
| dc.subject | o-minimality | |
| dc.subject | convex definable sets | |
| dc.subject | types over models | |
| dc.subject | cuts in ordered structures | |
| dc.subject | real closed fields | |
| dc.subject | model theory | |
| dc.title | Remarks on weak o-minimality | |
| dc.type | Article |