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Small theories of Boolean ordered o-minimal structures

Published online by Cambridge University Press:  12 March 2014

Roman Wencel
Roman Wencel*
Affiliation:
Mathematical Institute, University of Wrocław, PL. Grunwaldzki 2/4, 50-384 Wrocław, Poland, E-mail: [email protected]
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Abstract

We investigate small theories of Boolean ordered o-minimal structures. We prove that such theories are ℵ0-categorical. We give a complete characterization of their models up to bi-interpretability of the language. We investigate types over finite sets, formulas and the notions of definable and algebraic closure.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 4 , December 2002 , pp. 1385 - 1390
Copyright
Copyright © Association for Symbolic Logic 2002

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References

REFERENCES

[1]Baisalov, Y., Small o-minimal theories, preprint.Google Scholar
[2]Mayer, L., Vaught's conjecture for o-minimal theories, this Journal, vol. 53 (1988), pp. 146–159.Google Scholar
[3]Newelski, L. and Wencel, R., Definable sets in Boolean ordered o-minimal structures I, this Journal, vol. 66 (2001), pp. 1821–1836.Google Scholar
[4]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
[5]Toffalori, C., Lattice ordered o-minimal structures, Notre Dame Journal of Formal Logic, vol. 39 (1998), pp. 447–463.CrossRefGoogle Scholar