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What new axioms could not be

Dialectica 56 (2):109–124 (2002)

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  1. Canonical universes and intuitions about probabilities.Randall Dougherty & Jan Mycielski - 2006 - Dialectica 60 (4):357–368.
    This paper consists of three parts supplementing the papers of K. Hauser 2002 and D. Mumford 2000: There exist regular open sets of points in with paradoxical properties, which are constructed without using the axiom of choice or the continuum hypothesis. There exist canonical universes of sets in which one can define essentially all objects of mathematical analysis and in which all our intuitions about probabilities are true. Models satisfying the full axiom of choice cannot satisfy all those intuitions and (...)
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