Generic Families and Models of Set Theory with the Axiom of Choice
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چکیده
Let M be a countable transitive model of ZFC and i be a countable M -generic family of Cohen reals. We prove that there is no smallest transitive model A' of ZFC that either M u A ç N or A/U {A} ç N . h is also proved that there is no smallest transitive model N of ZFC~ (ZFC theory without the power set axiom) such that M U {A} ç N . It is also proved that certain classes of extensions of M obtained by Cohen generic reals have no minimal model.
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تاریخ انتشار 2010