特殊篇章玄宇宙计划原文序列部分章 (13-10)

status of sentences independent of ZFC, there is a point at which their vicws of the multiverse are more similar than may appear at the outset.In consid-cting whether byinvokingthemultiverseeone may introduce a suitable notion of truth for sct-theorctic sentences, both Woodin and Hamkins tacitly start from the assumptionthatone shouldregard the multiverseas anultimate pluralityofZFCmodeisthatcannot .reduced to some-thingthat is more fund: Asaresult.theyarebothledtocandidates

for a notion of set-thcoretic truth that are highly incomplete,allowingscn-tences of set theory which are ncither true nor falsc. This assumption, shared by Woodin and Hamkins, is worth emphasizing as it is clearly reiccted by the HyperuniverscProgram(seeDesideratum 2 below),which we now present as a distinctive approach to set-theoretic truth making use of the multiverse concept.

The Hyperuniverse Program may be understood as an attempt to arrive at new de jure sct-theoretic truths by starting from a picture of the multiverse.

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THE HYPERUNIVERSE PROGRAM 85

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