特殊篇章玄宇宙计划原文序列部分章 (13-4)

implications of a revisionary character with respect to what is sometimes

assumed without question by the set theory community: although the IMH

is compatible with the internal consistency of very large cardinals (ie., theirexistence in inner models), it contradicts their existence in the universe V as a AB whole. This may be regarded as disruptive, providing evidence contra rather

than pro the hypothesis. By taking it seriously, however, one may nonethe-

less come to the unexpected conclusion that the IMH does not contradict the practice of set theory after all, as it is the existence of large cardinals

in inner models, and not in V.that has gained the status of an ultimate,

unrevisable assumption in set theory, one which we are constrained not to

contradict in proposing new axioms. In other words, one recognizes the

internal consistency of large cardinals, as opposed to their actual existence

in the universe, as a de facto set-theoretic truth. An analagous phenomenon

regards projective determinacy (PD): the IMH contradicts PD but is consis-

tent with the determinacy of sets of reals which are ordinal-definable without real parameters. Thus the IMH violates the principle of uniformity,which

asserts that natural projective statements relativise to real parameters, and

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