On the Nonexistence of Free Complete Boolean Algebras

Author: Hales, Alfred Washington

Year: 1962

Degree: Dissertation (Ph.D.)

Advisor: Dilworth, Robert P.

Committee Member: Unknown, Unknown

Option: Mathematics

DOI: 10.7907/1ZW8-ES89

Abstract

Rieger asked in 1951 if there exists a free complete Boolean algebra on ω complete generators. Crawley and Dean proved in 1955 that there does not exist a free complete lattice on three complete generators, but their method does not extend to Boolean algebras. In this thesis Rieger's question is answered in the negative. The following more general result is then proved. Let γ be an infinite regular cardinal. Then there does not exist a free complete weakly (γ, ∞) distributive Boolean algebra on γ complete generators.

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