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The set-theoretic universe, as described by the standard Zermelo-Fraenkel axioms of set theory plus the Axiom of Choice (ZFC), provides the standard ontology for mathematics. However, the ZFC axioms are insufficient for answering many fundamental mathematical questions involving infinite sets, such as the Continuum Hypothesis, Lebesgue's measure extension problem, regularity properties for projective sets of real numbers, etc. We will argue that additional axioms of set theory asserting thedoi:10.3390/proceedings2010045 fatcat:kp2dllccjnb5vnnpm4yr2pqj4y