Well-founded Boolean ultrapowers as large cardinal embeddings

Abstract

Boolean ultrapowers extend the classical ultrapower construction to work with ultrafilters on any complete Boolean algebra, rather than only on a power set algebra. When they are well-founded, the associated Boolean ultrapower embeddings exhibit a large cardinal nature, and the Boolean ultrapower construction thereby unifies two central themes of set theory---forcing and large cardinals---by revealing them to be two facets of a single underlying construction, the Boolean ultrapower.

40 pages. This article was the topic of first author's tutorial lecture series at the Young Set Theorists Workshop at the Hausdorff Center for Mathematics in Konigswinter near Bonn, Germany, March 2011. Discussion forum for this paper at http://jdh.hamkins.org/boolean-ultrapowers

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