Vol. 35, No. 2, 1970

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ISSN: 0030-8730
Countable Boolean algebras as subalgebras and homomorphs

Timothy Edwin Cramer

Vol. 35 (1970), No. 2, 321–326
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
Authors
Timothy Edwin Cramer