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Construction of saturated quasi-minimal structure

Published online by Cambridge University Press:  12 March 2014

Masanori Itai ,
Akito Tsuboi  and
Kentaro Wakai
Masanori Itai
Affiliation:
Department of Mathematical Sciences, Tokai University, 1117 Kitakaname, Hiratsuka, Kanagawa, 259-1292, Japan, E-mail [email protected]
Akito Tsuboi
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki, 305, Japan, E-mail: [email protected]
Kentaro Wakai
Affiliation:
Department of Mathematical Sciences, Tokai University, 1117 Kitakaname, Hiratsuka, Kanagawa, 259-1292, Japan, E-mail: [email protected]
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Abstract

The notion of quasi-minimal structures was denned by B. Zil'ber as a natural generalization of minimal structures. Inspired by his work, we study here basic model theoretic properties of quasi-minimal structures. Main result is the construction of ω-saturated quasi-minimal models under ω-stability assumption.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 1 , March 2004 , pp. 9 - 22
Copyright
Copyright © Association for Symbolic Logic 2004

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References

REFERENCES

[1]Baldwin, J. T., Fundamentals of Stability Theory, Springer, 1988.Google Scholar
[2]Hodges, W., Model Theory, Cambridge University Press, 1993.CrossRefGoogle Scholar
[3]Itai, M. and Wakai, K., On quasi-minimal structures, Kokyuroku of the Research Institute of Mathematical Sciences in Kyoto, vol. 1213 (2001), pp. 50–54.Google Scholar
[4]Itai, M. and Wakai, K., Quasi-minimal structures and uncountable categoricity, Proceedings of the School of Sciences, vol. 37 (2002), pp. 1–8, Tokai University.Google Scholar
[5]Kunen, K., Set Theory, North Holland, 1980.Google Scholar
[6]Maesono, H., A remark on quasi-minimal structures, a talk given in Model theory meeting at Okayama University (Japan) on 12 21, 2001.Google Scholar
[7]Zil'ber, B., Dimensions and homogeneity in mathematical structures, Connections between Model Theory and Algebraic and Analytic Geometry, Quaderni di Matematica, vol. 6, Dipartimento di Matematica, Seconda Università di Napoli, 2000, pp. 131–148.Google Scholar