As part of a Young Academy Distinguished Lecture at the Austrian Academy of Sciences I gave a talk on October 9, 2024, in the Festsaal of the Austrian Academy of Sciences. This distinguished lecture was given jointly with Jan von Plato (University of Helsinki) and W. Hugh Woodin (Harvard University). See also the here (in German).

A Scenario for Solving 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 strong evidence provided by recent advances in Set Theory indicating that it is indeed the likely candidate Gödel was aiming for.

Here you can watch the recording of the Young Academy Distinguished Lecture.

Some pictures taken by Grigorii Stepanov: