特殊篇章玄宇宙计划原文序列部分章 (12-6)

mutually related (some universes may be,eg,forcing extensions, ground

models, or rank initial segments of others), and one may justifiably choose

elements of the hyperuniverse that are “prefcrable"in terms of this com-

parison. These are explicitly identified with the universes that, with respect

to those to which they are related, satisfy principles such as maximality or

omniscience.

Before considering how an element of the hyperuniverse may succeed in

being maximal.let us mention a danger of selecting universes according to

principles and criteria derived from an unbiascd look at the hyperuniversc.

In doing so one may be led to the adoption of first-order statements which contradictde facto set-thcoretic truth.Let us give an example One may

wish to make a selection of preferred universes based on a principle of min- AB) imaliry.One's criterion would therefore be that preferred universes should be as small as possible.This criterion may lead to the choice of just one uni-verse, the minimal model of ZFC, which would have as an implication that the statement that set models of ZFC do not exist expresses a property of V.This is however in obvious conflict with set-theoretic practice.i.e.,the exis-

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