Mathematical logic, algebra and number theory

On self-definable subsets of $\aleph_0$-categorical weakly o-minimal structures

B. Sh. Kulpeshov

Institute for Problems of Informatics and Control Sciences, Almaty

Abstract: The present paper concerns the generalization of the notion of o-minimality: weak o-minimality originally studied by D. Macpherson, D. Marker and Ch. Steinhorn in [1]. We study self-definable sets of an $\aleph_0$-categorical weakly o-minimal structure, and the main result is a criterion for goodness of every self-definable subset in an $\aleph_0$-categorical weakly o-minimal structure (Theorem 2.3).

Keywords: weak o-minimality, $\aleph_0$-categoricity, self-definable set.

UDC: 510.67

MSC: 03C64

Received July 25, 2012, published September 10, 2012

Language: English