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A remark on Martin's Conjecture

  • Su Gao (a1)

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.

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References

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[H]Hodges, W., Model theory, Cambridge University Press, Cambridge, 1993.
[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. 181187.
[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..
[W]Wagner, C. M., On Martin's conjecture, Annals of Mathematical Logic, vol. 22 (1982), pp. 4767.

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