特殊篇章玄宇宙计划原文序列部分章 (13-12)

for certain members of the hyperuniverse over others, thereby obtaining a

selection of preferred universes. The requirement that the multiverse bc

well-defined is a necessary condition for this selection process to be possible,

which would not be the case were the multiverse ill-defined or open-ended.

DESIDERATUM 2. The hyperuniverse is not an ultimate plurality. One can

express preferences for certain members of it according to criteria based on justified principles.

Another key point in the Hyperuniverse Program is that first-order prop-erties which are true across preferred universes of the hyperuniverse are truc

in V.

DESIDERATUM 3. Any first-order property of V is reflected into a countable transitive model of ZFC which is a preferred member of the hyperuniverse.

An important conscqucnce of Desideratum 3 is that, while the criteria

for preferred universes formulated within the Hyperuniverse Program may

be non first-order(indeed the criteria that we will introduce in Section 3

arc not—they quantify over the entire hyperuniverse), nonetheless in the

Hyperuniverse Program one arrives at first-order axioms for set theory, these

being the first-order truths shared by the preferred universcs.

In justifying Desideratum 3 one may invoke the downward Lowenheim-

Skolcm theorem, which, however, per se only implies that there must be

members of the hyperuniverse into which V first-order reflects. That these

数学联邦政治世界观提示您：看后求收藏（同人小说网http://tongren.me），接着再看更方便。