特殊篇章玄宇宙计划原文序列部分章 (10-6)

consist in its fruitfulness in consequences, its "shedding light upon a wholediscipline", and its yielding “powerful methods for solving given problems"

([9]. p.183). Mathematical results (facts “not known at Cantor's time") are

also invoked in the attempt to explain the prediction that Cantor's conjecture

will turn out to be wrong. Thus, the moral of [9] is that in formulating axiom

candidates for set theory, one not only is committed to the search for general

motivating principles that justify them, but one must also take into account

a corpus of already existing and accepted mathematical results, upon which

the new axiom(s) should shed light, or at the very least, not irreconcilably

contradict.

The approach that we present here shares many features, though not all. ofGödel's program for new axioms.Let us briefly illustrate it.The Hyperuni-

verse Program is an attempt to clarify which first-order set-theoretic state- AB) ments (beyond ZFC and its implications) are to be regarded as true in V. bycreating a context in which different pictures of the set-theoretic universe can

be compared. This context is the hyperuniverse, defined as the collection of all

countable transitive models of ZFC. The comparison of such models evokes

principles(principles of maximaliry and onniscience, as we will name two

of them) that suggest criteria for preferring. on justifiable grounds,certain

universes of sets over others.³ Starting from criteria for preferred universes,

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