Citation
Hales, Alfred Washington (1962) On the Nonexistence of Free Complete Boolean Algebras. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1ZW8-ES89. https://resolver.caltech.edu/CaltechTHESIS:08012011-122250596
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.
| Item Type: | Thesis (Dissertation (Ph.D.)) |
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| Subject Keywords: | (Mathematics) |
| Degree Grantor: | California Institute of Technology |
| Division: | Physics, Mathematics and Astronomy |
| Major Option: | Mathematics |
| Thesis Availability: | Public (worldwide access) |
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| Thesis Committee: |
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| Defense Date: | 1 January 1962 |
| Record Number: | CaltechTHESIS:08012011-122250596 |
| Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:08012011-122250596 |
| DOI: | 10.7907/1ZW8-ES89 |
| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 6561 |
| Collection: | CaltechTHESIS |
| Deposited By: | Tony Diaz |
| Deposited On: | 19 Aug 2011 23:29 |
| Last Modified: | 30 Nov 2023 00:22 |
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