特殊篇章玄宇宙计划原文序列部分章 (13-6)

dance of ZFC models has recently led to the introduction of the multiverse

as a new set-theoretic notion, and to related discussions about whether the

multiverse may represent the proper starting point foraddressing questions

concerning truth in set theory. Depending on one's view as to which ZFC models should enter into it, quite different pictures of the multiverse have been suggested in the literature. Diverging views have been expressed as well as to how the multiverse may work as a proper framework for pronouncing

on matters of set-theoretic truth. In this section we will review existing al-

ternative proposals concerning the multiverse and present the hyperuniverse

as an optimal realization of the multiverse concept.

Both Woodin and the second author have used the term multiverse for

collections of universes obtained from one or more initial models of ZFC ) via some method for manipulating them. In particular, in [23] Woodin starts

from countable transitive models M of ZFC, and takes the multiverse around

M to be the collcction gencrated by closing under set-generic extensions

and set-generic ground models (this is what Woodin calls the (ser-)generic

multiverse gencrated from M).⁹ Also V is regarded by Woodin so that a

(set-)generic multiverse may be generated from it.To this purpose one con-siders (set-)gencric extensions as Boolean valued models, i.e., models having

the form V ᴮ,where B is a complete Boolean algebra. In contrast to this

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