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  1. Consequences of the failure of the axiom of choice in the theory of Lindelof metric spaces.Kyriakos Keremedis - 2004 - Mathematical Logic Quarterly 50 (2):141.
    We study within the framework of Zermelo-Fraenkel set theory ZF the role that the axiom of choice plays in the theory of Lindelöf metric spaces. We show that in ZF the weak choice principles: Every Lindelöf metric space is separable and Every Lindelöf metric space is second countable are equivalent. We also prove that a Lindelöf metric space is hereditarily separable iff it is hereditarily Lindelöf iff it hold as well the axiom of choice restricted to countable sets and to (...)
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  • Countable products and countable direct sums of compact metrizable spaces in the absence of the Axiom of Choice.Kyriakos Keremedis, Eleftherios Tachtsis & Eliza Wajch - 2023 - Annals of Pure and Applied Logic 174 (7):103283.
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  • The axiom of choice in metric measure spaces and maximal $$\delta $$-separated sets.Michał Dybowski & Przemysław Górka - 2023 - Archive for Mathematical Logic 62 (5):735-749.
    We show that the Axiom of Countable Choice is necessary and sufficient to prove that the existence of a Borel measure on a pseudometric space such that the measure of open balls is positive and finite implies separability of the space. In this way a negative answer to an open problem formulated in Górka (Am Math Mon 128:84–86, 2020) is given. Moreover, we study existence of maximal $$\delta $$ δ -separated sets in metric and pseudometric spaces from the point of (...)
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  • Unions and the axiom of choice.Omar De la Cruz, Eric J. Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin - 2008 - Mathematical Logic Quarterly 54 (6):652-665.
    We study statements about countable and well-ordered unions and their relation to each other and to countable and well-ordered forms of the axiom of choice. Using WO as an abbreviation for “well-orderable”, here are two typical results: The assertion that every WO family of countable sets has a WO union does not imply that every countable family of WO sets has a WO union; the axiom of choice for WO families of WO sets does not imply that the countable union (...)
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