特殊篇章玄宇宙计划原文序列部分章 (10-9)

cribed independently of set-thcoretic practice.Instead “true in V” is meant

as a facon de parler that only conveys information about set-theorists'epis-

temic attitudes, as a description of the status that certain statements have or AB are expected to have in set-theorists'eyes. Sentences “true in V”are meant

to be sentences that are or should be regarded by set-theorists as definitive.

i.e,ultimate and not revisable.Within the Hyperuniverse Program two sorts

of statements qualify for this status. The first are those sct-thcorctic statc-

ments that, due to the role that they play in the practice of set theory and.

more gencrally, of mathematics, should not be contradicted by any further

candidate for a set-theoretic statement that may be regarded as ultimate and

not revisable. Let us call these statements "de facto”set-thcoretic truths.

The axioms of ZFC and the consistency of ZFC + large cardinal axioms are

examples of such truths.But secondly,within the Hyperuniverse Program,

one is ready to regard as true in statements that, beyond not contradicting

de facto set-theoretic truth, obey a condition for truth explicitly established

at the outset. Let us call these "de jure” set-theoretic truths. The condition

which they obey is that they are sentences that hold in all preferred universes

of the hyperuniverse. The latter, in turn, is not meant as an independent,

well-determined reality, but as a mathematical construct, produced along

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