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Construction of saturated quasi-minimal structure

  • Masanori Itai (a1), Akito Tsuboi (a2) and Kentaro Wakai (a3)

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.

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[1]Baldwin, J. T., Fundamentals of Stability Theory, Springer, 1988.
[2]Hodges, W., Model Theory, Cambridge University Press, 1993.
[3]Itai, M. and Wakai, K., On quasi-minimal structures, Kokyuroku of the Research Institute of Mathematical Sciences in Kyoto, vol. 1213 (2001), pp. 5054.
[4]Itai, M. and Wakai, K., Quasi-minimal structures and uncountable categoricity, Proceedings of the School of Sciences, vol. 37 (2002), pp. 18, Tokai University.
[5]Kunen, K., Set Theory, North Holland, 1980.
[6]Maesono, H., A remark on quasi-minimal structures, a talk given in Model theory meeting at Okayama University (Japan) on 12 21, 2001.
[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. 131148.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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