James sequences and Dependent Choices
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Marianne Morillon
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Article
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2005
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John Wiley and Sons
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English
β 240 KB
We prove James's sequential characterization of (compact) reflexivity in set-theory ZF + DC, where DC is the axiom of Dependent Choices. In turn, James's criterion implies that every infinite set is Dedekind-infinite, whence it is not provable in ZF. Our proof in ZF + DC of James' criterion leads us