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On the set-theoretic strength of the existence of disjoint cofinal sets in posets without maximal elements
Mathematical Logic Quarterly 62 (3):155-176 (2016)
Abstract
In set theory without the Axiom of Choice math formula, we study the deductive strength of the statements math formula, math formula, math formula, and math formula. Among various results, we prove that none of the above statements is provable without using some form of choice, math formula is equivalent to math formula, math formula + math formula implies math formula, math formula does not imply math formula in math formula, math formula does not imply math formula in math formula and math formula is strictly weaker than math formula in math formula.Other Versions
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Citations of this work
On ramsey’s theorem and the existence of infinite chains or infinite anti-chains in infinite posets.Eleftherios Tachtsis - 2016 - Journal of Symbolic Logic 81 (1):384-394.
MA(ℵ0) restricted to complete Boolean algebras and choice.Eleftherios Tachtsis - 2021 - Mathematical Logic Quarterly 67 (4):420-431.
On the minimal cover property and certain notions of finite.Eleftherios Tachtsis - 2018 - Archive for Mathematical Logic 57 (5-6):665-686.
References found in this work
Zermelo-Fraenkel consistency results by Fraenkel-Mostowski methods.David Pincus - 1972 - Journal of Symbolic Logic 37 (4):721-743.
On the strength of the Sikorski extension theorem for Boolean algebras.J. L. Bell - 1983 - Journal of Symbolic Logic 48 (3):841-846.
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