I am invited to give an online talk on January 31, 2025 in the Poset-G seminar, a monthly online seminar with the aim to foster interaction and cooperation between philosophers of set theory and set-theorists.

Scenarios for attacking Gödel’s Problem

After proving that not all statements in mathematics can be proven or disproven from the accepted ZFC axioms, Gödel raised the question whether natural statements, such as Cantor’s continuum hypothesis, can be decided via extending the axiomatic framework by axioms of large infinities. While this question has been answered in the negative, the problem of finding good axioms that decide natural mathematical statements remains open. There is a compelling candidate for an axiom that could solve Gödel’s problem: V = Ultimate L. We motivate and describe this candidate together with the Sealing scenario as well as recent set theoretic advances in this area.