特殊篇章玄宇宙计划原文序列部分章 (13-2)

independent questions. Moreover the techniques needed to establish the

cxistencc of preferred universes are provided by existing developments in

set theory or by new developments inspired by the program which extend

existing developments. There is another reason, however, for the Hyperuni-verse Program to explicitly call upon set-theoretic developments, albeit in ancgative way. When declaring the intention of extending ZFC so as to settlc independent questions, one also requires that one be as nbiased as possiblc

as to the way such questions should be settled and as to which principles

and criteria for preferred universes onc should formulate. In particular, the

latter must not be chosen at the outset so as to be apt for settling questions

independent of ZFC, or for mecting the necds of some particular arca of

existing set-theoretic r should specific mathematical hypotheses

be invoked in formulating such principles and criteria (c.g., large cardinal

or forcing axioms). The rationale bchind unbiasedness is twofold. On the

one hand, one wants to be as cautious as possible as to what sct-thcoretic

developments beyond ZFC belong to the realm of de facto set-theoretic

truth.Endorsing this attitude mcans doing justice to the fact that disparate

views have been advanced within the set-theoretic community on this mat-

ter. Secondly, one aims at formulating principles and criteria starting from

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