Weakly o-minimal nonvaluational structures
نویسندگان
چکیده
منابع مشابه
Weakly o-minimal nonvaluational structures
A weakly o-minimal structure M = (M,≤,+, . . .) expanding an ordered group (M,≤, +) is called non-valuational iff for every cut 〈C,D〉 of (M,≤) definable in M, we have that inf{y − x : x ∈ C, y ∈ D} = 0. The study of non-valuational weakly o-minimal expansions of real closed fields carried out in [MMS] suggests that this class is very close to the class of o-minimal expansions of real closed fie...
متن کاملOn 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 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 کاملWeakly O-minimal Structures and Real Closed Fields
A linearly ordered structure is weakly o-minimal if all of its definable sets in one variable are the union of finitely many convex sets in the structure. Weakly o-minimal structures were introduced by Dickmann, and they arise in several contexts. We here prove several fundamental results about weakly o-minimal structures. Foremost among these, we show that every weakly o-minimal ordered field ...
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 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: Annals of Pure and Applied Logic
سال: 2008
ISSN: 0168-0072
DOI: 10.1016/j.apal.2008.01.009