特殊篇章玄宇宙计划原文序列部分章 (10-7)

one applies the principle that first-order statements that hold across all pre-

ferred universes (hopefully including solutions to independent questions)

also hold in V (an assumption based partly on the downward Lowenheim-

Skolem theorem), and adopts these statements as new axioms of set theory.

This being, in a nutshell, the Hyperuniverse Program, one clearly sees that

it shares the fundamental aim of Gödel's program of extending ZFC by newset-theoretic axioms resulting from "a more profound understanding of basic

concepts underlying logic and mathematics".In fact,within the Hyperuni-

verse Program one formulates principles and criteria for preferred universes

that are suggested by a logico-mathematical analysis of the hyperuniverse.

Also, Gödel's suggestion to consider a “maximn property of the system of

all sets" for extending ZFC is addressed by this program. Indeed maximality

works well as a principle inspiring criteria for preferred universes.Moreover,

in both Gödel's program and the Hyperuniverse Program, one seeks to find

solutions to independent questions in a way that may be regarded as ultimate

and not revisable, and hence may be regarded as definitive or true in V，the

universe of all sets.

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"The formulation of criteria for preferred universes is not an casy task. In particular the

possibility of conflicting desiderata to be imposed on preferred universes of sets cannot be

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