特殊篇章玄宇宙计划原文序列部分章 (10-5)

It is by invoking the criterion of success as contributing to a decision about

the truth of a candidate for an axiom for set theory that the way is opened in

＿＿＿＿＿

　² By “small large cardinals" are here meant large cardinals whose existence is compatible

with the axiom of constructibility V = L.Gödel pronounces on one of them.the axiom

stating the existence of an inaccessible cardinal,as follows:

The simplest of thesc "strong axioms of infinity" asscrts the cxistence of inac-

cessible numbers (and of oumbers inaccessiblc in the stronger sensc)＞ℵ₀. The

lutter axiom, roughly ans nothing else but that the totality of sets

obtainable by exclusive use of the procedure of formation of sets expressed in the

other axioms forms again a set (and therefore a new basis for further applications

of these processes). ([9], p.182)

The axiom stating the existence of a measurable cardinal, as well as its incompatibility with the

axiom of constructibility, was known to Gödel as he wrote [10].However, Gödel apparently

did not consider this axiom as implied by the coacept of set (see[10], footaote 16).

　3 Thhs cosecnd dowaliouded Wam 143.207.2.50 on Tae.27 Aog 2013 17 31:39 PM

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　THE HYPERLNIVERSE PROGRAM 79

[9] for bringing considerations of a purely mathematical character into the

discussion of proposals for new axioms. The success of an axiom is meant to

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