特殊篇章玄宇宙计划原文序列部分章 (13-11)

　that faithfully summarizes the full plethora of results obtainable in contem-porary sct theory. That one focuses on well-founded models of ZFC when using this approach just amounts to expressing the twofold conviction that the axioms of ZFC are de facto set-thcoretic truths and that it is only the well-founded models of this theory that provide plausible pictures of the set-thcoretic universe. The Hyperuniverse Program thus begins by asserting thatthe multiverse should satisfy a maximality and a well-definedness criterionthat only the collcction of all countable transitive models of ZFC can mect.

More precisely:

DESIDERATUM 1.The multiverse should be as rich as possible but it should not be an ill-defined or open-ended multiplicity.

In stating this, onc has two aims. First, onc is motivated by the fact that

the methods for creating well-founded universes existing in contemporary

set thcory go well beyond set-forcing or class-forcing (hence the multivcrsc

should include more than set- or class-generic extensions and ground mod-cls). Since the hyperuniverse, the collection of all countable transitive modcls AB) of ZFC, is closed under all possible universe-creation methods, one is led to identifying the multiverse with it. Second, requiring in Desideratum I that

the multiverse be given a precise mathematical formulation enables one to put it to work for the aim of enriching the realm of set-thcoretic truth. This

is done in the Hyperuniverse Program by formulating justifiable preferences

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