Forcing extensions of the nonstandard universe
- 491 Downloads
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.
Unable to display preview. Download preview PDF.