特殊篇章玄宇宙计划原文序列部分章 (10-2)

In recent years, different research programs, motivated by independence phenomenahave been formulated in set theory The stage for most of them has been set by Gödel's program for new axioms, announced in [9]at a time when the independence of the Continuum Hypothesis from ZFC could only be (correctly) conjcctured. [9], and its revised and extendedversion[10].have played a fundamental role in the debate concerningthe foundations of set theory. In defense of the views there expressed. Gödel invoked philosophical considerations on the nature of mathematics,anal- ysis of logico-mathematical concepts, and technical arguments of a purely mathematical character.Similar ingredients can be found in most of the subsequent proposals for overcoming independence results.

Gödel's program is worth a closer look. As a fundamental motivation for the program of extending ZFC through the addition of new axioms, the conviction is expressed in [9]that it is possible to give a final answer

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　Received January 31，2012.

Key words and phrases independence, large cardinals, multiverse, Platonism and Anti- platonism, set-theoretic truth.

　Both authors were supported by the Austrian Science Fund (FWF), Project P22430-N13.The first author was also supported by the European Science Foundation by an Exchange Grant within the framework of the ESF activity ‘New Frontiers of Infinity: Mathematical. Philosophical and Computational Prospecta".

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