A polarized partition relation for cardinals of countable cofinality
نویسندگان
چکیده
منابع مشابه
A Partition Relation Using Strongly Compact Cardinals Sh761
If κ is strongly compact and λ > κ and λ is regular (or alternatively cf(λ) ≥ κ), then ` 2 ́+ → (λ+ ζ) θ holds for ζ, θ < κ. 2000 Mathematics Subject Classification. 2000 Math Subject Classification: 03E02. I would like to thank Alice Leonhardt for the beautiful typing. Research of the author was partially supported by the United States-Israel Binational Science Foundation. Publ.761. Latest Rev...
متن کاملPartition 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...
متن کاملCofinality and Measurability of the First Three Uncountable Cardinals
This paper discusses models of set theory without the Axiom of Choice. We investigate all possible patterns of the cofinality function and the distribution of measurability on the first three uncountable cardinals. The result relies heavily on a strengthening of an unpublished result of Kechris: we prove (under AD) that there is a cardinal κ such that the triple (κ, κ+, κ++) satisfies the stron...
متن کاملCovering of the Null Ideal May Have Countable Cofinality
We prove that it is consistent that the covering number of the ideal of measure zero sets has countable cofinality.
متن کاملWeak Partition Properties for Infinite Cardinals. I
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2007
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-07-09143-5