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A remark on Martin's Conjecture

Published online by Cambridge University Press:  12 March 2014

Su Gao
Su Gao*
Affiliation:
Department of Mathematics, California Institute of Techology, Pasadena, CA 91125, USA, E-mail: [email protected]
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Abstract

We prove that the strong Martin conjecture is false. The counterexample is the first-order theory of infinite atomic Boolean algebras. We show that for this class of Boolean algebras, the classification of their (ω + ω)-elementary theories can be reduced to the classification of the elementary theories of their quotient algrbras modulo the Frechét ideals.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 1 , March 2001 , pp. 401 - 406
Copyright
Copyright © Association for Symbolic Logic 2001

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References

REFERENCES

[H]Hodges, W., Model theory, Cambridge University Press, Cambridge, 1993.CrossRefGoogle Scholar
[I]Iverson, P., The number of countable isomorphism type of complete extensions of the theory of Boolean algebras, Colloquium Mathematicum, Polish Academy of Sciences, vol. 62, (1991), pp. 181–187.CrossRefGoogle Scholar
[K]Koppelberg, S., Handbook of Boolean Algrbras, vol. 1, North-Holland, Amsterdam-New York, 1989, volums I–III edited by Monk, J. D. and Bonnet, R..Google Scholar
[W]Wagner, C. M., On Martin's conjecture, Annals of Mathematical Logic, vol. 22 (1982), pp. 47–67.CrossRefGoogle Scholar