Countable Boolean algebras as subalgebras and homomorphs

Timothy Edwin Cramer

Vol. 35 (1970), No. 2, 321–326

DOI: 10.2140/pjm.1970.35.321

Abstract

The problem of classifying all countable Boolean algebras appears to be impossible to solve. This paper considers the following problem. Given a class 𝒞 of countable Boolean algebras, which is closed under isomorphisms, characterize the classes of

1. all Boolean algebras which have subalgebras in 𝒞;
2. all subalgebras of members of 𝒞;
3. all homomorphs of members of 𝒞;
4. all Boolean algebras which have homomorphs in 𝒞.

Definitive characlerizations are obtained for the first three classes (Theorems 7, 8, and 9), and a representation of the Iast class is obtained when 𝒞 is the class of all countabte Boolean algebras (Theorem II).

Mathematical Subject Classification

Primary: 06.60

Milestones

Received: 5 November 1969

Revised: 23 January 1970

Published: 1 November 1970