特殊篇章玄宇宙计划原文序列部分章 (13-8)

Class-forcing and hyperclass-forcing have the same status as sel-forcing within set theory.

Moreover, by restricting to set-forcing and assuming the existence of large cardinals, one

artificially avoids a real difficulty of any unbiascd scarch for new set-thcoretic axioms, that of dealing with justifiable principles that may destroy large cardinal axioms.

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84 TATIANA ARRIGONIAND SY-DAVID FRIEDMAN

forcing. Also Hamkins has recently formulated a view of the multiverse,

apparently dissociating from both Woodin and the second author. What in

[11] is referred to as the multiverse is, in fact, not a collection of ZFC mod-

cls that can be gencrated from initial universes by closing under specified

procedures. Rather,the multiverse is described as the multitudeconsist-

ing of all set-thcorctic universes that have been constructed so far and may

be produced in the future, possibly including non well-founded models and

models of systems other than ZFC. The result is a heterogencous open-ended

plurality, of which no overall unified description can be given.

Nor is there consensus among set-theorists as to whether and how the

multiverse should be regarded as a context for determining questions of

truth. Hamkins' proposal of a heterogencous open-ended multiversc, for

instance, is accompanied by the twofold invitation to abandon the “dream

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