Weak Distributivity Implying Distributivity
Dan Hathaway

TL;DR
This paper demonstrates that certain weak distributivity conditions on complete Boolean algebras imply stronger distributivity properties, with implications for large cardinal assumptions.
Contribution
It establishes new conditions under which weak distributivity implies full distributivity in Boolean algebras, extending previous results.
Findings
Weak $(eth_eta, eta)$-distributivity implies $(eth_eta, 2)$-distributivity.
Weak $(2^ heta, heta)$-distributivity with large cardinal assumptions implies full $( heta, 2)$-distributivity.
Results connect weak distributivity conditions with large cardinal properties.
Abstract
Let be a complete Boolean algebra. We show, as an application of a previous result of the author, that if is an infinite cardinal and is weakly -distributive, then is -distributive. Using a parallel result, we show that if is a weakly compact cardinal such that is weakly -distributive and is -distributive for each , then is -distributive.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Rings, Modules, and Algebras
