Are There Enough Injective Sets?

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Are There Enough Injective Sets?

The axiom of choice ensures precisely that, in ZFC, every set is projective: that is, a projective object in the category of sets. In constructive ZF (CZF) the existence of enough projective sets has been discussed as an additional axiom taken from the interpretation of CZF in Martin-Löf’s intuitionistic type theory. On the other hand, every non–empty set is injective in classical ZF, which arg...

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ژورنال

عنوان ژورنال: Studia Logica

سال: 2012

ISSN: 0039-3215,1572-8730

DOI: 10.1007/s11225-011-9365-8