Remarks on Levy's reflection axiom
作者:
Martin Dowd,
期刊:
Mathematical Logic Quarterly
(WILEY Available online 1993)
卷期:
Volume 39,
issue 1
页码: 79-95
ISSN:0942-5616
年代: 1993
DOI:10.1002/malq.19930390111
出版商: WILEY‐VCH Verlag Berlin GmbH
关键词: Levy's reflection axiom;Higher types;Mahlo cardinals;Greatly Mahlo cardinals;Continuum hypothesis
数据来源: WILEY
摘要:
AbstractAdding higher types to set theory differs from adding inaccessible cardinals, in that higher type arguments apply to all sets rather than just ordinary ones. Levy's reflection axiom is justified, by considering the principle that we can pretend that the universe is a set, together with methods of Gaifman [8]. We reprove some results of Gaifman, and some facts about Levy's reflection axiom, including the fact that adding higher types yields no new theorems about sets. Some remarks on standard models are made. An obvious strengthening of Levy's axiom to higher types is considered, which implies the existence of indescribable cardinals. Other remarks about larger cardinals are made; some questions of Gloede [9]are settled. Finally we argue that the evidence forV=Lis strong, and that CH is certainly true. MSC: 03E30, 03E55.
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