特殊篇章玄宇宙计划原文序列部分章 (12-9)

Ordinal (or vertical) maximality has a long history in set theory. It is also known as a higher-order reflection principle, and has been shown to imply (and to justify) the existence of “small”large cardinals (i.e.large cardi- nal notions consistent with V = L such as inaccessibles, weak compacts, w-Erdos cardinals, ...).¹³ Power set maximality, instead, has been only recently formulated. In fact it is equivalent to the IMH.which formally speaking states that by passing to an outermodelof ∪.internal consistency remains unchanged，i.e,the set of parameter-free sentences which hold in some inner model of ∪ is not increased. Assessing the compatibility of power set maximality with de facto set-theoretic truths is no trivial mat- ter. For the IMH refutes the existence of inaccessible cardinals as well as projective determinacy (PD) (see [7]).These implications have forced a re-examination of the roles of large cardinals and determinacy in set- thcoretic practice. As a result onc sees that power set maximality maybe compatible with de facto set-theoretic truths after all. For, if one accepts that the role of large cardinals in set theory is correctly described by saying that their existence in inner models, and not their existence in V, is a de facto set-theoretic truth, and that the importance of PD is captured by its parameter-free version, then the compatibility of power set maximality with set-theoretic practice is restored:the IMH is in fact consistent both with inner models of very large cardinals and with parameter-free PD (indeed with OD-determinacy without real paramcters).¹⁴ We will returm to the

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。