特殊篇章玄宇宙计划原文序列部分章 (13-3)

　 ⁵An example of this will be given in Section 3, where the criterion of power set mapcimaliry

is modificd so as to be compatible with the criterion of ordinal maximality.

⁶See,e.g..[22] and [19] for different positions on the status of large cardinal axioms or thc

axiom of detcrminacy AD˪[ʀ] in contemporary set theory.

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82 TATIANA ARRIGONI AND SY-DAVID FRIEDMAN

an analysis of the hyperuniverse which focus exclusively on its most general

features. As a result, the principles chosen and the criteria derived from

them are expected to yield a justified selection of preferred universes on the

solc basis of onc's acquaintancc with the most basic aspects of set thcory.

A surprise is that,unbiasedness notwithstanding, the Hyperuniverse Pro-gram leads to results that strongly affect our understanding of the corpus

of already existing set-theoretic developments. This is the case, eg., if one

adopts the Inner Model Hypothesis (IMH), as formulated in [7]1, as a criterionfor preferred universes, providing a suitable description of what it means for a countable transitive modcl of ZFC to be maximal (fixing the ordinals).

This hypothesis settles many questions independent of ZFC, but also has

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