A Note on Weakly O-Minimal Structures and Definable Completeness
نویسندگان
چکیده
منابع مشابه
On Definable Skolem Functions in Weakly O-Minimal nonvaluational Structures
We prove that all known examples of weakly o-minimal non-valuational structures have no de nable Skolem functions. We show, however, that such structures eliminate imaginaries up to de nable families of cuts. Along the way we give some new examples of weakly ominimal non-valuational structures.
متن کاملTopological properties of sets definable in weakly o-minimal structures
The paper is aimed at studying the topological dimension for sets definable in weakly o-minimal structures in order to prepare background for further investigation of groups, group actions and fields definable in the weakly o-minimal context. We prove that the topological dimension of a set definable in a weakly o-minimal structure is invariant under definable injective maps, strengthening an a...
متن کاملDefinable choice for a class of weakly o-minimal theories
Given an o-minimal structure M with a group operation, we show that for a properly convex subset U , the theory of the expanded structure M′ = (M, U) has definable Skolem functions precisely when M′ is valuational. As a corollary, we get an elementary proof that the theory of any such M′ does not satisfy definable choice. §
متن کاملA survey on groups definable in o-minimal structures
Groups definable in o-minimal structures have been studied for the last twenty years. The starting point of all the development is Pillay’s theorem that a definable group is a definable group manifold (see Section 2). This implies that when the group has the order type of the reals, we have a real Lie group. The main lines of research in the subject so far have been the following: (1) Interpret...
متن کاملOn N0-Categorical Weakly o-Minimal Structures
@0-categorical o-minimal structures were completely described in 4], and are essentially built up from copies of the rationals as an ordered set by`cutting and copying'. Here we investigate the possible structures which an @0-categorical weakly o-minimal set may carry, and nd that there are some rather more interesting (and not o-minimal) examples. We show that even here the possibilities are l...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 2007
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1179323268