منابع مشابه
Indescribable cardinals without diamonds
where E is a stationary subset of some cardinal ~. Jensen (cf. I-D2]) showed that if K is regular and uncountable and V=L then O~,E holds. Following his work, a number of applications of this principle and its modifications have been developed which are wide ranging and not restricted to set theory (cf. [-D1]). Jensen had also discovered that various large cardinals carry diamond sequences with...
متن کاملDiamonds on large cardinals
Acknowledgements I want to express my sincere gratitude to my supervisor Professor Jouko Väänänen for supporting me during all these years of getting acquainted with the intriguing field of set theory. I am also grateful to all other members of the Helsinki Logic Group for interesting discussions and guidance. Especially I wish to thank Do-cent Tapani Hyttinen who patiently has worked with all ...
متن کاملThe Indestructability of the Order of the Indescribable Cardinals
Hauser, K., The indescribability of the order of the indescribable cardinals, Annals of Pure and Applied Logic 57 (1992) 45-91. We prove the following consistency results about indescribable cardinals which answer a question of A. Kanamori and M. Magidor (cf. [3]). Theorem 1.1 (m 22, n 22). CON(ZFC+ 3~, K’ (K is Ii: indescribable, K’ is XF indescribable, and K < K’)) j CON(ZFC + fl> n: + GCH). ...
متن کاملViolating the Singular Cardinals Hypothesis Without Large Cardinals
Easton proved that the behavior of the exponential function 2 at regular cardinals κ is independent of the axioms of set theory except for some simple classical laws. The Singular Cardinals Hypothesis SCH implies that the Generalized Continuum Hypothesis GCH 2 = κ holds at a singular cardinal κ if GCH holds below κ. Gitik and Mitchell have determined the consistency strength of the negation of ...
متن کاملRowbottom cardinals without the Axiom of Choice
We show that for all natural numbers n, the theory “ZF +DCאn + אω is a Rowbottom cardinal carrying a Rowbottom filter” has the same consistency strength as the theory “ZFC + There exists a measurable cardinal”. In addition, we show that the theory “ZF + אω1 is an ω2-Rowbottom cardinal carrying an ω2-Rowbottom filter and ω1 is regular” has the same consistency strength as the theory “ZFC + There...
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ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 1992
ISSN: 0933-5846,1432-0665
DOI: 10.1007/bf01627508