终极L（数学论文）一 (14-1)

注意：一共划分（1/2）篇章！

NEW LARGE-CARDINAL AXIOMS AND THE ULTIMATE-L PROGRAM

RUPERT MCALLUM

ABSTRACT.We will consider a number of new large-cardinal prop- erties, the c-tremendous cardinals for each limit ordinal α＞0，the hyper-tremendous cardinals，the-enormous cardinals for each limit ordinal α＞0，and the hyper-enormous cardinals. For limit ordinals a α＞0，the α-tremendous cardinals and hyper-tremendous cardinals have consistency strength between I3 and I2. The α- enormous cardinals and hyper-enormous cardinalshaveconsistency strength greater than I0, and also all the large-cardinal axioms discussed in the second part of Hugh Woodin's paper on suitable extender models, not known to be inconsistent with ZFC and of greater consistency strength than I0.Ralf Schindler and Victoria Gitman have developed the notion of a virtual large-cardinal prop- erty, and a clear sense can be given to the notions of“virtuallv

x-enormous"and“virtually hyper-enormous”. On the assumption that V＝HOD，a measurable cardinal can be shown to be vir- tually hyper-enormous. Using a definition of Ultimate-L given in Section 6, claimed to be the correct definition on the assumption that there is a proper class of -enormous cardinals for each limit ordinal α＞0，it can be shown that，if V is equal to Ultimate-L in the sense of that definition,then it follows that a virtually w-enormous cardinal is alimitof Ramsey cardinals.

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。