A Remark On Martin's Conjecture

Journal of Symbolic Logic 66 (1):401-406 (2001)
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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 -elementary theories can be reduced to the classification of the elementary theories of their quotient algebras modulo the Frechet ideals.

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