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On the Nonexistence of Free Complete Boolean Algebras


Hales, Alfred Washington (1962) On the Nonexistence of Free Complete Boolean Algebras. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1ZW8-ES89.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mathematics)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Dilworth, Robert P.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1962
Record Number:CaltechTHESIS:08012011-122250596
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6561
Deposited By: Tony Diaz
Deposited On:19 Aug 2011 23:29
Last Modified:30 Nov 2023 00:22

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