Abstract
The partition property for measures on Pℋλ was formulated by analogy with a property which Rowbottom [1] proved was possessed by every normal measure on a measurable cardinal. This property has been studied in [2], [3], and [4]. This note summarizes [5] and [6], which contain results relating the partition property with the extendibility of the measure and with an auxiliary combinatorial property introduced by Menas in [4]. Detailed proofs will appear in [5] and [6].
Highlights
The partition property for measures on P % was formulated by analogy with a property which Rowbottom [I] proved was possessed by every normal measure on a
Is super compact if it is k-supercompact Vk >_. This concept was introduced in [7] because of its analogy with the notion of a measurable cardinal. (A cardinal is measurable if there exists a :P()
By analogy with Rowbottom’s theorem, it was natural to conjecture that every normal measure on P k would have the partition property
Summary
The partition property for measures on P % was formulated by analogy with a property which Rowbottom [I] proved was possessed by every normal measure on a. Where K,k are infinite cardinals with < k P % denotes the set p c_k llpl < 31 A measure, on P is a 10,11-valued function defined on subsets of P % satisfying A measure on P X is called normal if, in addition, it satisfies (A cardinal is measurable if there exists a :P()
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