特殊篇章玄宇宙计划原文序列部分章 (5-4)

ommendation to consider some maximum property of the system of all sets for the purpose of extending ZFC. Since maximality is used in the Hyperuni-versc Program as a motivating principle for criteria for preferred universes we advocated above that this program meets Gödel's recommendation.Of

coursc, while claiming this,we are aware of the fact that the considerations

concerning maximality developed within the Hyperuniverse Program are

of a different nature than those invoked in alternative proposals for new

set-theoretic axioms. This applies, in particular to proposals to the efTect

that ZFC should be cnlarged through the addition of suitable large cardinal

hypotheses,as these being faithful to our expectations concerning the mix/-

mim character of the universe of all sets. Consider the following quotition

by H.Wang ([21].p.553):

We believe that the collection of all ordinals is very ‘long' and cach

power set (of an infinite) set is very ‘thick'. Hence any axioms to

such effect arc in accordance with our intuitive concept.

By giving, as Wang does, the length of the ordinals and the thickness of

powersets as examplesof maximumproperties of the systenofallsets.

数学联邦政治世界观提示您：看后求收藏（同人小说网http://tongren.me），接着再看更方便。