Abstract
AbstractIt is a long standing open problem whether or not the Axiom of Countable Choice implies the fragment of Martin's Axiom either in or in . In this direction, we provide a partial answer by establishing that the Boolean Prime Ideal Theorem in conjunction with the Countable Union Theorem does not imply restricted to complete Boolean algebras in . Furthermore, we prove that the latter (formally) weaker form of and the Δ‐system Lemma are independent of each other in .We also answer open questions from Tachtsis [16] which concern the status of restricted to complete Boolean algebras in certain Fraenkel–Mostowski permutation models of and we strengthen some results from the above paper.
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