特殊篇章玄宇宙计划原文序列部分章 (10-2)

In particular, in the Hyperuniverse Program V plays the role of an out-

come that one can only approach by starting from the hyperuniverse as the

most suitable instantiation of the multiverse notion. The fact that within theHyperuniverse Program one endorses a multiverse perspective is explained as by Woodin, who says that “the refinements of Cohen's method of forcing in the decades since its initial discovery and the resulting plethora of prob-lems shown to be unsolvable, have in a practical sense almost compelled one to adopt” a multiverse position in contemporary set theory ([23). p.103).

Consider that, from a multiverse perspective,one works not with a unique

"system of all sets” but with many different ones, and deals with them as

meta-mathematical constructions, as models. From a multiverse perspective

one is thus naturally led to understand the expression “maximal properties

of the system of all sets” in terms of meta-mathematical features revealed by

comparing set-theoretic models. This is what is done in the Hypcruniversc

Program. Criteria like vertical and horizontal maximality are the rigorous

cxpression of what it means for an clement of the hyperuniverse, i.e., a count-able transitive model of ZFC, to display “maximum properties”, To put it in other terms, no need is seen in the Hyperuniverse Program to make existen-tial asscrtions concerning V in order to bc faithful to the idea that the system

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