# The Tarski Lectures

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 and built up here 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 this country and in 1942 accepted a position as Lecturer at 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 Lecturer in 2022-23 will be given by Professor Richard Shore**, Richard Shore was on the faculty at Cornell University from 1974 to 2020 at which point he retired as Goldwin Smith Professor of Mathematics Emeritus. During those years he held visiting appointments at Harvard, The Hebrew University, M.I.T., MSRI (Berkeley), National University of Singapore, The University of Chicago, University of Sienna and others institutions.

In addition to his personal research grants, Shore has been a principal investigator for binational grants with mathematicians in Greece, Israel, Italy and New Zealand. Shore has been a speaker at the ICM (1983) and the ICLMPS (1999) as well as many other venues. He was the Godel Lecturer for the ASL in 2009. He has served the ASL in many capacities including President (2001-04). Since 2008, he has been the Publisher of the ASL. Among his other editorial work, Shore was the founding managing editor of the Bulletin of Symbolic Logic (1993-2000). He was also a member of the board of Project Euclid, an early online mathematical publishing platform, from its launch in 2002 until 2013. Among the eighteen thesis students he supervised, four (with one as secondary advisor) have won the Sacks Prize for the year's best thesis in logic.

**Lecture 1 of 2 **(April 24, 2023 @ 4:10–5:00 pm, UC Berkeley Campus, Location: Physics 3)**: **

Mathematics: A Multiverse: The basic question that reverse mathematics attempts to address is how hard is it to prove particular theorems or carry out particular constructions of ordinary classical mathematics. Hard not in the sense of how many hours, days or years or cups of coffee it took a mathematician or many mathemati-cians to prove the theorem but hard in some more mathematical sense. This talk will be an introduction to the subject with hints of a new view. We primarily consider two related standard criteria of hardness and the relations between. One is based on the strength of formal systems of (second order) arithmetic in which theorems can be proved. The second is recursion theoretic and based on the computational complexity of the objects the theorems assert exist. We will also briefly discuss relations to common philosophical approaches to the foundations of mathematics as well as a number of newer approaches that vary the logic and formal systems allowed in the first case and variations on computation complexity notions in the second. Finally, we present a glimpse of a new setting for the universe of reverse mathematics. It is an analysis the sort that has become common for recursion theoretic degree structures but yields drastically different results for proof theoretic strength.

**Lecture 2 of 2: **(April 26, 2023 @ 4:10–5:00 pm, Location: 60 Evans Hall):

Reverse Mathematics: A Global View: We view the structure of reverse mathematics as a degree structure similar to that of the Turing degrees, DT with the ordering of Turing reducibility,T .We will discuss four theorms during this lecture. We can characterize the few s that fall into each of the first three classes in terms of notions familiar in the general study of theories. This analysis was prompted by my thinking about what I should talk about in these lectures. Much to my surprise, after I had worked out most of these results I discovered that Tarski had proven many of them some ninety years ago and so long before the rise of reverse mathematics.

Past Tarski Lecturers

1989 Dana Stewart Scott

1990 Willard Van Orman Quine

1991 Bjarni Jónsson & H. Jerome Keisler

1992 Donald Anthony Martin

1993 Alec James Wilkie

1994 Michael O. Rabin

1995 Hilary Putnam

1996 Ehud Hrushovski

1997 Menachem Magidor

1998 Angus John Macintyre

1999 Patrick Suppes

2000 Alexander A. Razborov

2001 Ronald Bjorn Jensen

2002 Boris Zilber

2003 Ralph Nelson McKenzie

2004 Alexander S. Kechris

2005 Zlil Sela

2006 Solomon Feferman

2007 Harvey M. Friedman

2008 Yiannis N. Moschovakis

2009 Anand Pillay

2010 Gregory Hjorth

2011 Johan van Benthem

2012 Per Martin-Löf

2013 Jonathan Pila

2014 Stevo Todorcevic

2015 Julia F. Knight

2016 William Tait

2017 Lou van den Dries

2019 Thomas Hales

2020 Zoe Chatzidakis (not delivered)

2023 Richard Shore