In set theory, Berkeley cardinals are certain large cardinals suggested by Hugh Woodin in a seminar at the University of California, Berkeley in about 1992. A Berkeley cardinal is a cardinal κ in a model of Zermelo–Fraenkel set theory with the property that for every transitive set M that includes κ and α < κ, there is a nontrivial elementary embedding of M into M with α < critical point < κ. Berkeley cardinals are a strictly stronger cardinal axiom than Rei… http://www.fedoa.unina.it/11570/1/cutolo_raffaella_29.pdf

LARGECARDINALSBEYONDCHOICE - JSTOR

Nettet若 \delta 是正则的以及对于所有的 club C\subseteq \delta ： Cub Berkeley cardinal-- \mathcal{S}\left( M \right) 内的所有成员在临界点 {\sf crit}\left( j \right)\in C 处使得 \delta\in M 且存在一个 j\in \mathcal{S}\left( M \right).-- 其极限为 limit Cub Berkeley cardinal。 Corollary. 若 \kappa 为 extendible 的 ... NettetAbstract. We continue the study of the virtual large cardinal hierarchy, initiated in [GS18], by analysing virtual versions of superstrong, Woodin, Vopěnka, and Berkeley … cheap flights from tulsa to cleveland

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Nettet5. mai 2024 · The differences that I can see is that for Berkeley cardinals, the critical points are required to be unbounded in δ while for club Berkeley cardinals there must be critical points in every club, and that club Berkeley cardinals must be regular. Since the ordinals between η and δ, for any η < δ, constitute a club, it appears that club ... Nettet1. jan. 2003 · See e.g. Exercise 26.10 in [9].7 Note that this also shows that virtually club Berkeley cardinals and virtually Berkeley cardinals are equiconsistent, which is an open question in the non-virtual ... Nettet2. jul. 2024 · Choiceless large cardinals and set-theoretic potentialism. We define a potentialist system of ZF-structures, that is, a collection of possible worlds in the language of ZF connected by a binary accessibility relation, achieving a potentialist account of the full background set-theoretic universe . The definition involves Berkeley cardinals, the ... cheap flights from tulsa to ontario ca