[bibtex key=HamkinsSeabold:BooleanUltrapowers]

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.

The topic of this article was the focus of my tutorial lecture series at the Young Set Theorists Workshop at the Hausdorff Center for Mathematics in Königswinter near Bonn, Germany, March 21-25, 2011.

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