Hausdorff Medal for Gabriel Goldberg

Award ceremony at the European Set Theory Conference in Münster

The 6th Hausdorff Medal was awarded to Gabriel Goldberg (UC Berkeley). The prize is awarded every two years for the most influential work in set theory published in the five years preceding the medal. The ceremony took place at the European Set Theory Conference in Münster on 16 September 2024. Philip Welch, President of the European Set Theory Society, presented the medal. The ceremony included a laudatio by W. Hugh Woodin and a talk by the medal winner.

Philip Welch, President of the European Set Theory Society, presented the medal to Gabriel Goldberg.
Philip Welch, President of the European Set Theory Society, presented the medal to Gabriel Goldberg.
© MM/vl

With the medal, the committee honours the contribution Gabriel Goldberg has made through his recent book "The Ultrapower Axiom". Goldberg has abstracted the idea of using the comparison process - which holds in canonical inner models for large cardinals built to date, and hopefully in the future, to encapsulate a key ingredient of comparison as the “Ultrapower Axiom” (UA). It asserts that a form of amalgamation holds for ultrapowers of V. UA then holds in all canonical inner models. A host of results can be derived from assuming UA: the linearity of the Ketonen order on countably complete measures (to which it is equivalent); the linearity of the Mitchell order. Given the existence of a supercompact cardinal, V becomes a generic extension of HOD. Moreover, the GCH holds above a supercompact cardinal. It also advances our understanding on the well-known fraught relationship between supercompactness and strong compactness: under UA the least strongly compact is supercompact and any strongly compact is either supercompact or a limit of such.

  • G. Goldberg, "The Ultrapower Axiom". de Gruyter series in Logic and its Applications, vol 10, 2022.

Other subsequent papers mentioned by the committee to show Goldberg's outstanding contribution:

  • G. Goldberg, "Strongly compact cardinals and ordinal definability". JML, Vol. 24, No. 1, Apr. 2024.
  • G. Goldberg & F. Schlutzenberg, "Periodicity in the cumulative hierarchy". JEMS, DOI 10.4171/JEMS/1318, 2023.
  • G. Goldberg. "The uniqueness of elementary embeddings". Journal of Symbolic Logic, accepted.

Gabriel Goldberg is an assistant professor at UC Berkeley working in set theory, interested in large cardinals, inner models, and forcing. He received his PhD in Mathematics at Harvard University.

Links:
Webpage of Gabriel Goldberg
European Set Theory Conference 2024
European Set Theory Society

With the medal, the committee honours the contribution Gabriel Goldberg has made through his recent book "The Ultrapower Axiom".
© MM/vl
Laudatio by Prof. Dr. W. Hugh Woodin.
Laudatio by W. Hugh Woodin (Harvard).
© MM/vl I W.H.Woodin at ESTC