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ArticleOriginal scientific text

Title

Representing free Boolean algebras

Authors 1, 2

Affiliations

  1. Department of Mathematics, York University, North York, Ontario, Canada M3J 1P3
  2. Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, U.S.A.

Abstract

Partitioner algebras are defined in [2] and are natural tools for studying the properties of maximal almost disjoint families of subsets of ω. In this paper we investigate which free algebras can be represented as partitioner algebras or as subalgebras of partitioner algebras. In so doing we answer a question raised in [2] by showing that the free algebra with ℵ1 generators is represented. It was shown in [2] that it is consistent that the free Boolean algebra of size continuum is not a subalgebra of any partitioner algebra.

Bibliography

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm141/fm14112.pdf

Fundamenta Mathematicae
1992/141/1
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Pages:
21-30
Main language of publication
English
Received
1991-01-21
Accepted
1991-08-19
Published
1992
Exact and natural sciences