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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:[email protected]
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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

REFERENCES

[1] Baizhanov, B. S., The types in the weakly o-minimal theories, preprint, 1996.Google Scholar
[2] Dickmann, M. A., Elimination of quantifiers for ordered valuation rings, Proceedings of the 3rd Easter model theory conference at Gross Koris, Berlin, 1985.Google Scholar
[3] Kulpeshov, B. Sh., Weak o-minimality of a linearly ordered structure, Researches in theory of algebraic systems (Nurmagambetov, T., editor), Karagandinskiy Gosudarstvennyy Universitet, Karaganda, 1995, pp. 61–67.Google Scholar
[4] Kulpeshov, B. Sh., Some corollaries of the criterion of weak o-minimality and rank of convexity, Proceedings of informatics and control problems institute (Aidarkhanov, M. and Baizhanov, B., editors), Gylym, Almaty, 1996, pp. 142–160.Google Scholar
[5] Macpherson, D., Marker, D., and Steinhorn, C., Weakly o-minimal structures and real closed fields, preprint, 1993.Google Scholar
[6] Pillay, A., Some remarks on definable equivalence relations in o-minimal structures, this Journal, vol. 51 (1986), pp. 709–714.Google Scholar
[7] Pillay, A. and Steinhorn, C., Definable sets in ordered structures I, Transactions of the American Mathematical Society, vol. 295 (1986), pp. 565–592.CrossRefGoogle Scholar
[8] van den Dries, L., Remarks on Tarski's problem concerning (r, +, *, exp), Logic colloquim '82 (Lolli, G., Longo, G., and Marcja, A., editors), North-Holland, Amsterdam, 1984, pp. 97–121.Google Scholar