Hausdorff medal 2015

The second Hausdorff medal was awarded by the European Set Theory Society on August 26, 2015, at the fifth European Set Theory Conference, held at the Isaac Newton Institute in Cambridge, to Ronald Jensen (Humboldt University, Berlin) and John Steel (UC Berkeley) for their work K without the measurable.

Statement read by the president of the European Set Theory Society, Istvan Juhasz, at the award ceremony:

Ladies and gentlemen, dear friends and colleagues!

It is my pleasure and privilege, as president of the European Set Theory Society, to announce the winner of the Hausdorff medal. This is awarded by the Board of Trustees of the European Set Theory Society at the biennial European Set Theory Conference for the most influential published work in set theory in the last five years.

Nominations for the Hausdorff medal 2015 were solicited from the members of the Society last fall. Five very worthy nominations were deliberated by the prize committee which consisted of the Board of Trustees augmented with the winner of the previous medal, Hugh Woodin.

After long and serious discussion the unanimous decision was reached that the second Hausdorff medal is awarded to the paper

K without the measurable, The Journal of Symbolic Logic, Volume 78, Issue 3 (2013), 708-734

by Ronald Jensen and John Steel.

Before handing over the medals and the diplomas that go with them to the winners, please allow me to briefly review the winning work.

The construction of core models originates in the seminal work of Dodd and Jensen of just about 40 years ago. Since that time the constructions have been vastly developed and the machinery in its various incarnations is the main tool for showing the necessity of large cardinals for independence proofs. Even more striking is the use of core model methods to prove outright implications of, for example, of determinacy.

Despite all this progress, an absolutely fundamental question remained unresolved. What is the strongest core model which can be constructed just in ZFC? More precisely, suppose there is no inner model with a Woodin cardinal; does then K exist? Jensen and Steel solved this problem in the paper K without the measurable.

The Jensen-Steel construction of K is best possible (having been done just within ZFC) and is therefore a seminal milestone in the entire subject of core models and inner model theory. It marks in some sense the conclusion of a line of investigation which began with Jensen’s Covering Lemma.

It already has many applications, for example as a corollary of their construction, one obtains the equiconsistency of ‘ZFC + There is a saturated ideal on \omega_1’ with ‘ZFC + There is a Woodin cardinal’.

Photo by Hugo Nobrega
John Steel (left), Istvan Juhasz (centre), Ronald Jensen (right), photo by Hugo Nobrega

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