On the nonexistence of free complete Boolean algebras

[摘要] Rieger asked in 1951 if there exists a free complete Booleanalgebra on ω complete generators. Crawley and Dean proved in1955 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.

[发布机构] University:California Institute of Technology;Department:Physics, Mathematics and Astronomy

[关键词] Mathematics