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Weakly o-minimal structures and some of their properties

Published online by Cambridge University Press:  12 March 2014

B. SH. Kulpeshov
B. SH. Kulpeshov*
Affiliation:
Informatics and Control Problems Institute, Ministry of Science—Academy of Science, 480021, UL. Pushkina 125, Almaty, Kazakstan. E-mail:LNS@ipic.academ.alma-ata.su
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 4 , December 1998 , pp. 1511 - 1528
Copyright
Copyright © Association for Symbolic Logic 1998

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References

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