## Journal of Symbolic Logic

### A Remark on Martin's Conjecture

Su Gao

#### 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 ($\omega + \omega$)-elementary theories can be reduced to the classification of the elementary theories of their quotient algebras modulo the Frechet ideals.

#### Article information

Source
J. Symbolic Logic, Volume 66, Issue 1 (2001), 401-406.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183746378

Mathematical Reviews number (MathSciNet)
MR1825192

Zentralblatt MATH identifier
1002.03029

JSTOR

#### Citation

Gao, Su. A Remark on Martin's Conjecture. J. Symbolic Logic 66 (2001), no. 1, 401--406. https://projecteuclid.org/euclid.jsl/1183746378