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Erschienen in:
2004 | OriginalPaper | Buchkapitel
Forcing extensions of the nonstandard universe
verfasst von : Vladimir Kanovei, Michael Reeken
Erschienen in: Nonstandard Analysis, Axiomatically
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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Recall that the class L[I] of sets constructible from internal sets was employed in Chapter 5 to obtain some consistency theorems. For instance Theorem 5.5.8 implies that it is consistent with HST that I-infinite internal sets of different I-cardinalities are necessarily non-equinumerous. It would be in the spirit of mathematical foundations to ask whether the negation of this sentence, that is the existence of equinumerous I-infinite internal sets of different I-cardinalities, is also consistent.