特殊篇章玄宇宙计划原文序列部分章 (5-3)

It is worth observing that, although the realization of the Hyperuni-verse Program presented in this paper fails to resolve many interesting

I me uPIt m/sjum lesang

TATIANA ARRICONI AND SY-DAVID FRIEDMAN 92

ZFC-independent questions and raises issues that call for further investi-gation (starting with the consistency of the Synthesis Conjecture),this by no means undermines the overall validity and mathematical fruitfulness of the program. Quite the contrary, the rescarch outcomes obtained and the questions entailed by the developments inspired by the Hyperuniverse Pro- gram attest to its mathematical potential and speak of its promise for the future,as further principles(such as omniscience) that motivate criteria for preferred universes are analyzed and discovered, and a synthesis is sought for them in conjunction with maximality.

§5. Appendix: the byperuniverse program, maximality, large cardinals and PD. This Appendix is devoted to a closer examination of the rela- tion of the Hyperuniverse Program to alternative proposals for extending set-thcoretic truth (beyond ZFC and other de facto true set-theoretic state- ments), in particular to large cardinals and Projective Determinacy (PD) as candidates for axioms of set theory.

Gödel's Program for new axioms, sketched in Section 1, includes the rec-

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。