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Some two-cardinal results for O-minimal theories

Published online by Cambridge University Press:  12 March 2014

Timothy Bays
Timothy Bays*
Affiliation:
Department of Philosophy, Yale University, P. O. Box 208306, New Haven, CT 06520-8306, USA, E-mail: [email protected]
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Abstract

We examine two-cardinal problems for the class of O-minimal theories. We prove that an O-minimal theory which admits some (κ, λ) must admit every (κ′, λ′). We also prove that every “reasonable” variant of Chang's Conjecture is true for O-minimal structures. Finally, we generalize these results from the two-cardinal case to the δ-cardinal case for arbitrary ordinals δ.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 2 , June 1998 , pp. 543 - 548
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[1] Bays, Timothy, Multi-cardinal phenomena in stable theories, Ph.D. thesis , University of California, Los Angeles, 1994.Google Scholar
[2] Knight, Julia, Pillay, Anand, and Steinhorn, Charles, Definable sets in ordered structures II, Transactions of the American Mathematical Society, vol. 295 (1986), pp. 593–605.Google Scholar
[3] Lachlan, Alistair, A property of stable theories, Fundamenta Mathematica, vol. 77 (1972), pp. 9–20.10.4064/fm-77-1-9-20Google Scholar
[4] Pillay, Anand, An introduction to stability theory, Clarendon Press, Oxford, 1983.Google Scholar
[5] Pillay, Anand and Steinhorn, Charles, Definable sets in ordered structures I, Transactions of the American Mathematical Society, vol. 295 (1986), pp. 565–592.Google Scholar
[6] Shelah, Saharon, Categoricity of classes of models, Ph.D. thesis , The Hebrew University, 1976.Google Scholar
[7] Vaught, Richard, A Löwenheim-Skolem theorem for cardinals far apart, The theory of models (Addison, John, Henkin, Leon, and Tarski, Alfred, editors), North-Holland, Amsterdam, 1965, pp. 390–401.Google Scholar