The Tarski Lectures

Alfred Tarski

Alfred Tarski profile

The Alfred Tarski Lectures are supported by an endowment fund established in memory of a man widely regarded as one of the four greatest logicians of all time. A superb teacher and influential scientific leader as well as a profound thinker, Alfred Tarski arrived in Berkeley in 1942 at the age of 41. Here, he built up what is often cited as the outstanding center for research in logic and the foundations of mathematics in the world.

Born in Warsaw in 1901, Tarski was educated in Polish schools and received his Ph.D. at the University of Warsaw in 1924. He served as a Docent and later as an Adjunct Professor at the University of Warsaw. He was visiting the U.S. when Germany invaded Poland in 1939. Unable to return home, he remained in the U.S. and in 1942 accepted a position as Lecturer at UC Berkeley. He became a full professor in 1946 and in 1958 founded the pioneering interdisciplinary Group in Logic and the Methodology Science. He retired in 1971 and died in October 1983 at the age of 82.

Of his numerous investigations, outlined in seven books and more than 300 other publications, Tarski was most proud of two: his design in 1930 of an algorithm to decide the truth or falsity of any sentence in the elementary theory of the field of real numbers and his path-breaking mathematical treatment in the early 1930's of the semantics of formal languages and the concept of truth.

The Tarski Lecture in 2024  will be given by Kobi Peterzil and Sergei Starchenko

Two Mathematicians sitting on a bench


In a series of papers we examined first the following question:  Given X \subseteq R^n definable in an o minimal structure, and given a lattice L in R^n, with pi: R^n> R^n / L, what can be said about the closure of pi(X) in the torus?

We then generalize the question in two directions: We replace R^n with a unipotent group G, replace the set X with a definable family {X_s} of subsets of G, and ask about the possible Hausdorff limits of {pi(X_s)} in the nilmanifold G /L.

As we shall describe in our talks, the answers combine the model theoretic machinery of types in o-minimal groups, with some cases of Ratner’s theorem in unipotent groups. The “flatness” of such types at infinity, together with the co-compactness of the lattices, gives rise to linear subspaces of R^n, or in the unipotent case, to algebraic subgroups of G associated to the set X, and the closure  and Hausdorff limits could be understood using those subgroups.

In the first talk we  describe the closure problem in tori,  using many examples.

In the second talk we explain some of the model theoretic ingredients which come up in the solution.

In the third talk we discuss generalizations to closures  in nil-manifolds and to Hausdorff limits.

1. Closures and flows in real tori: a model theoretic approach.

Monday April 22, 2024, Physics 3 - reception to follow in 1015 Evans

2. The interplay of o-minimality and discrete subgroups.

Wednesday April 24, 2024 Physics 3

3. From closures to Hausdorff limits, in  tori and nilmanifolds. 

Thursday April 25, Evans 60

Past Tarski Lecturers

Year Lecturer
2024 Kobi Peterzil & Sergei Starchenko
2023 Richard Shore
2020 Zoe Chatzidakis (not delivered)
2019  Thomas Hales
2017 Lou van den Dries
2016 William Tait
2015 Julia F. Knight
2014 Stevo Todorcevic
2013 Jonathan Pila
2012 Per Martin-Löf
2011 Johan van Benthem
2010 Gregory Hjorth
2009 Anand Pillay
2008 Yiannis N. Moschovakis
2007 Harvey M. Friedman
2006 Solomon Feferman
2005 Zlil Sela
2004  Alexander S. Kechris
2003 Ralph Nelson McKenzie
2002 Boris Zilber
2001 Ronald Bjorn Jensen
2000 Alexander A. Razborov
1999 Patrick Suppes
1998 Angus John Macintyre
1997 Menachem Magidor
1996 Ehud Hrushovski

Hilary Putnam

1994 Michael O. Rabin
1993 Alec James Wilkie
1992 Donald Anthony Martin
1991 Bjarni Jónsson & H. Jerome Keisler
1990 Willard Van Orman Quine
1989 Dana Stewart Scott