Well-founded Boolean ultrapowers as large cardinal embeddings

Joel David Hamkins; Daniel Evan Seabold

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arXiv · 1206.6075

Well-founded Boolean ultrapowers as large cardinal embeddings

Joel David Hamkins·Daniel Evan Seabold

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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.

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BibTeX RIS

Joel David Hamkins, Daniel Evan Seabold. 2012-06-26. Well-founded Boolean ultrapowers as large cardinal embeddings. https://arxiv.org/abs/1206.6075

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