## 2023

John Steel, University of California, Berkeley

The 10th Carol Karp Prize is awarded to John Steel for his work in set theory, especially for his book “A Comparison Process for Mouse Pairs”, Cambridge University Press, 2022. The fundamental contribution of the book is the theory of hod mice, which are objects that are used to characterize the universe of hereditarily ordinal definable sets of models of determinacy. Besides developing this theory, the book solves many problems well-known within the set theory community. Steel’s work has an incredible mathematical clarity and sophistication. It tackles deep and difficult theoretical problems that have fundamental applications in our understanding of set theoretic frameworks and links between them.

## 2018

Matthias Aschenbrenner, University of California, Los Angeles; Lou van den Dries, University of Illinois at Urbana-Champaign; Joris van der Hoeven, École Polytechnique

The ninth Carol Karp Prize was jointly awarded at the ASL North American Annual Meeting to Matthias Aschenbrenner, Lou van den Dries, and Joris van der Hoeven for their work in model theory, especially on asymptotic differential algebra and the model theory of transseries.

## 2013

Moti Gitik, Tel Aviv University; Ya’acov Peterzil, University of Haifa; Jonathan Pila, University of Oxford; Sergei Starchenko, University of Notre Dame; and Alex Wilkie, University of Manchester

The eighth Carol Karp Prize was jointly awarded to Moti Gitik for his work in set theory, especially applications of large-cardinal forcings to $pcf$-theory, and to Ya’acov Peterzil, Jonathan Pila, Sergei Starchenko and Alex Wilkie for their work in model theory, especially as applied to questions in number theory.

## 2008

Zlil Sela, Hebrew University

The recipient of the seventh Carol Karp Prize is Zlil Sela for his fundamental work connecting logic with geometric group theory. Among the consequences of his work are a proof that the class of finitely generated, torsion-free hyperbolic groups is closed under elementary equivalence, and a proof that any two nonabelian free groups are elementarily equivalent.

## 2003

Gregory Hjorth, University of California, Los Angeles and Alexander Kechris, California Institute of Technology

The sixth Carol Karp Prize was awarded at the ASL Annual Meeting to Gregory Hjorth and Alexander Kechris for their recent work on Borel equivalence relations, in particular for their results on turbulence and countable Borel equivalence relations.

## 1998

Ehud Hrushovski, Hebrew University

The recipient of the 1998 Karp Prize of the Association for Symbolic Logic was Ehud Hrushovski of the Hebrew University, Jerusalem, for his work on the Mordell-Lang Conjecture. This award was made by the Association on recommendation of the ASL Committee on Prizes and Awards.

## 1993

Ehud Hrushovski, Massachusetts Institute of Technology and Alex Wilkie, University of Oxford

The ASL Committee on Prizes and Awards selected Ehud Hrushovski, MIT, and Alex Wilkie, Oxford, as the recipients of the 1993 Karp Prize. Hrushovski was honored for his introduction of new methods in geometric stability theory; Wilkie was honored for proving the model completeness of the field of real numbers with the exponential function. The two prizes were awarded at a special session at the ASL Annual Meeting in March, at which John Baldwin and Angus Macintyre gave talks which summarized the accomplishments for which Hrushovski and Wilkie were being honored.

## 1988

Donald A. Martin and John R. Steel, University of California, Los Angeles; and W. Hugh Woodin, University of California, Berkeley

The ASL Committee on Prizes and Awards selected Donald A. Martin, UCLA, John R. Steel, UCLA, and W. Hugh Woodin, University of California, Berkeley as the recipients of the 1988 Karp Prize, “for their work establishing from the existence of a supercompact cardinal that the Axiom of Determinacy holds in the smallest transitive model of ZF containing all reals and all ordinals.”

## 1983

Saharon Shelah, Hebrew University

The 1983 Karp Prize was awarded to Saharon Shelah of the Hebrew University of Jerusalem, Israel, for his work on the number of nonisomorphic models of first order theories.

## 1978

Robert Vaught, University of California, Berkeley