منابع مشابه
On dp-minimal ordered structures
We show basic facts about dp-minimal ordered structures. The main results are: dp-minimal groups are abelian-by-finite-exponent, in a divisible ordered dp-minimal group, any infinite set has non-empty interior, and any theory of pure tree is dp-minimal.
متن کاملOn Minimal Ordered Structures
We partially describe minimal, first-order structures which have a strong form of the strict order property. An infinite first-order structure is minimal if its each definable (possibly with parameters) subset is either finite or co-finite. It is strongly minimal if the minimality is preserved in elementarily equivalent structures. While strongly minimal structures were investigated more closel...
متن کاملOn ordered minimal structures
Recall that a structure M is minimal if every definable (with parameters) subset of M is either finite or cofinite. The study of minimal partially ordered structures was initiated by Tanović in [4, 5]. The results from [4, 5] were essential in the proof by Tanović of the Pillay’s conjecture [1], which states that every countable structure in a countable language has infinitely many nonisomorphi...
متن کاملTame topology over dp-minimal structures
In this paper we develop tame topology over dp-minimal structures equipped with definable uniformities satisfying certain assumptions. Our assumptions are enough to ensure that definable sets are tame: there is a good notion of dimension on definable sets, definable functions are almost everywhere continuous, and definable sets are finite unions of graphs of definable continuous “multi-valued f...
متن کاملA monotonicity theorem for dp-minimal densely ordered groups
Dp-minimality is a common generalization of weak minimality and weak o-minimality. If T is a weakly o-minimal theory then it is dp-minimal (Fact 2.2), but there are dp-minimal densely ordered groups that are not weakly o-minimal. We introduce the even more general notion of inpminimality and prove that in an inp-minimal densely ordered group, every definable unary function is a union of finitel...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2011
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1305810758