A Remark on Martin's Conjecture
colorful horizontal rule

Su Gao

Abstract

We prove that the strong Martin conjecture is false. The counterexample is the first-order class of atomic Boolean algebras with infinitely many atoms. 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.

Table of Contents

  1. Introduction
  2. From algebras to quotients
  3. From quotients to algebras
  4. Some further problems
    References

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This paper is published in the Journal of Symbolic Logic 66 (2001), no. 1, 401-406.

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