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  1. MA(ℵ0) restricted to complete Boolean algebras and choice.Eleftherios Tachtsis - 2021 - Mathematical Logic Quarterly 67 (4):420-431.
    It 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 (...)
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  • On Martin's Axiom and Forms of Choice.Eleftherios Tachtsis - 2016 - Mathematical Logic Quarterly 62 (3):190-203.
    Martin's Axiom math formula is the statement that for every well-ordered cardinal math formula, the statement math formula holds, where math formula is “if math formula is a c.c.c. quasi order and math formula is a family of math formula dense sets in P, then there is a math formula-generic filter of P”. In math formula, the fragment math formula is provable, but not in general in math formula. In this paper, we investigate the interrelation between math formula and various (...)
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  • Powers of.Kyriakos Keremedis & Horst Herrlich - 1999 - Notre Dame Journal of Formal Logic 40 (3):346-351.
    It is shown that in ZF Martin's $ \aleph_{0}^{}$-axiom together with the axiom of countable choice for finite sets imply that arbitrary powers 2X of a 2-point discrete space are Baire; and that the latter property implies the following: the axiom of countable choice for finite sets, power sets of infinite sets are Dedekind-infinite, there are no amorphous sets, and weak forms of the Kinna-Wagner principle.
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  • Powers of 2.Kyriakos Keremedis & Horst Herrlich - 1999 - Notre Dame Journal of Formal Logic 40 (3):346-351.
    It is shown that in ZF Martin's -axiom together with the axiom of countable choice for finite sets imply that arbitrary powers 2X of a 2-point discrete space are Baire; and that the latter property implies the following: (a) the axiom of countable choice for finite sets, (b) power sets of infinite sets are Dedekind-infinite, (c) there are no amorphous sets, and (d) weak forms of the Kinna-Wagner principle.
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