WEAK DISTRIBUTIVITY IMPLYING DISTRIBUTIVITY
Copyright policy )WEAK DISTRIBUTIVITY IMPLYING DISTRIBUTIVITY
AbstractLet $B$ be a complete Boolean algebra. We show that if λ is an infinite cardinal and $B$ is weakly (λω, ω)-distributive, then $B$ is (λ, 2)-distributive. Using a similar argument, we show that if κ is a weakly compact cardinal such that $B$ is weakly (2κ, κ)-distributive and $B$ is (α, 2)-distributive for each α < κ, then $B$ is (κ, 2)-distributive.
- University of Denver United States
weakly compact cardinal, Large cardinals, complete Boolean algebra, weak distributivity, Mathematics - Logic, tower number, Cardinal characteristics of the continuum, Ordered sets and their cofinalities; pcf theory, FOS: Mathematics, Structure theory of Boolean algebras, distributive laws, Logical aspects of Boolean algebras, Logic (math.LO)
weakly compact cardinal, Large cardinals, complete Boolean algebra, weak distributivity, Mathematics - Logic, tower number, Cardinal characteristics of the continuum, Ordered sets and their cofinalities; pcf theory, FOS: Mathematics, Structure theory of Boolean algebras, distributive laws, Logical aspects of Boolean algebras, Logic (math.LO)
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