INTERPRETABLE SETS IN DENSE O-MINIMAL STRUCTURES
نویسندگان
چکیده
منابع مشابه
Topologizing interpretable sets in O-minimal Structures
Let M be a structure in some language. Assume M has elimination of imaginaries. Let X be a definable set. Definable will mean “definable with parameters.” By a definable topology, we mean a definable family of subsets {By ⊂ X}y∈Y which form the basis for some topology on X. The fact that these form a basis for a topology amounts to the claim that if y1, y2 have By1 ∩By2 6= ∅, then for every x ∈...
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The structure of definable sets and maps in dense elementary pairs of o-minimal expansions of ordered abelian groups is described. It turns out that a certain notion of “small definable set” plays a special role in this description. Introduction. In a classical paper [8] A. Robinson proved the completeness of the theory of real closed fields with a predicate for a proper dense real closed subfi...
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We study the theory of Lovely pairs of þ-rank one theories, in particular O-minimal theories. We show that the class of א0-saturated dense pairs of O-minimal structures studied by van den Dries [6] agrees with the corresponding class of lovely pairs. We also prove that the theory of lovely pairs of O-minimal structures is super-rosy of rank ≤ ω.
متن کاملNear Integral Points of Sets Definable in O Minimal Structures
Modifying the proof of a theorem of Wilkie, it is shown that if a one dimnsional set S is definable in an O minimal expansion of the ordered field of the reals, and if it is regularly exponentially near to many integral points, then there is an unbounded set, which is R definable without parameters, and which is exponentially near to S.
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2018
ISSN: 0022-4812,1943-5886
DOI: 10.1017/jsl.2018.50