On the partition property of measures on Pℋλ

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].

Keywords

• supercompact cardinals
• measures with the partition property
• extendible measures.