Partition relations for successor cardinals
نویسندگان
چکیده
منابع مشابه
Partition Relations for Successor Cardinals
This paper investigates the relations K+ --t (a): and its variants for uncountable cardinals K. First of all, the extensive literature in this area is reviewed. Then, some possibilities afforded by large cardinal hypotheses are derived, for example, if K is measurable, then K + + (K + K + 1, a): for every a < K +. Finally, the limitations imposed on provability in ZFC by L and by relative consi...
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Kanamori, A., Regressive partition relations, n-subtle cardinals, and Bore1 diagonalization, Annals of Pure and Applied Logic 52 (1991) 65-77. We consider natural strengthenings of H. Friedman’s Bore1 diagonahzation propositions and characterize their consistency strengths in terms of the n-subtle cardinals. After providing a systematic survey of regressive partition relations and their use in ...
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We give an exposition in modern language (and using partial orders) of Jech’s method for obtaining models where successor cardinals have large cardinal properties. In such models, the axiom of choice must necessarily fail. In particular, we show how, given any regular cardinal and a large cardinal of the requisite type above it, there is a symmetric extension of the universe in which the axiom ...
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Partition properties are perhaps the most fruitful of the various methods for defining and discussing large cardinals in set theory. In this paper we weaken in a natural way the most well known of these partition properties and examine the extent to which the cardinals defined remain "large." 1. 1.1. An area of set theory which has come under a great deal of study recently is that concerned wit...
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The assumption of [HM] and our assumption here, the existence of a strong partition cardinal, is moderately special. On the one hand, it violates the Axiom of Choice and is not relatively consistent with ZF (unlike AC and its negation). On the other hand, under the Axiom of Determinacy (AD), such cardinals are abundant and consistent with countable choice and DC, the principle of Dependent Choi...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1986
ISSN: 0001-8708
DOI: 10.1016/0001-8708(86)90049-6