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Article · Journal of Symbolic Logic · December 1, 1998

Weakly o-minimal structures and some of their properties

Beibut Kulpeshov
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Abstract

Abstract The main result of this paper is Theorem 3.1 which is a criterion for weak o-minimality of a linearly ordered structure in terms of realizations of 1-types. Here we also prove some other properties of weakly o-minimal structures. In particular, we characterize all weakly o-minimal linear orderings in the signature {<, =} . Moreover, we present a criterion for density of isolated types of a weakly o-minimal theory. Lastly, at the end of the paper we present some remarks on the Exchange Principle for algebraic closure in a weakly o-minimal structure.

Advanced Topology and Set TheoryRings, Modules, and AlgebrasMathematical and Theoretical Analysiso-minimalityexchange principlealgebraic closure

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