Set-theoretic Pluralism, Symposium I, July 12-17, 2016, at the University of Aberdeen. My talk will be the final talk of the conference.

**Abstract.** I shall discuss several bits of pluralism-inspired mathematics, including especially an account of Toshimichi Usuba’s recent proof of the strong downward-directed grounds DDG hypothesis, which asserts that the collection of ground models of the set-theoretic universe is downward directed. This breakthrough settles several of what were the main open questions of set-theoretic geology. It implies, for example, that the mantle is a model of ZFC and is identical to the generic mantle and that it is therefore the largest forcing-invariant class. Usuba’s analysis also happens to show that the existence of certain very large cardinals outright implies that there is a smallest ground model of the universe, an unexpected connection between large cardinals and forcing. In addition to these results, I shall present several other instances of pluralism-inspired mathematics, including a few elementary but surprising results that I hope will be entertaining.

Slides | Set-theoretic Pluralism Network | Conference program

I can’t wait to see this!

Thanks for your enthusiasm, Toby! I look forward to seeing you in Aberdeen.

Hope City University of New York will join the Set Theoretic Pluralism network partners too:

https://sites.google.com/site/pluralset/network-partners

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