Leo Harrington

Leo Harrington
Name	Leo Harrington
Birth date	1949
Birth place	Santa Monica, California
Fields	Mathematics, Set theory, Mathematical logic
Workplaces	University of California, Berkeley, University of California, Los Angeles, Dartmouth College
Alma mater	University of California, Berkeley
Doctoral advisor	Robert M. Solovay
Known for	Partition properties, reverse mathematics, inner model theory

Leo Harrington is an American mathematician noted for contributions to set theory, mathematical logic, and the foundations of mathematics. He is best known for collaborative results on determinacy, partition relations, and the interaction between large cardinals and descriptive set theory. Harrington's work influenced developments in inner model theory, recursion theory, and proof theory through collaborations with leading figures such as Donald A. Martin, Robert M. Solovay, William Hugh Woodin, and Gerald E. Sacks.

Early life and education

Harrington was born in Santa Monica, California, and raised in the Southern California region near Los Angeles. He attended public schools in the Los Angeles County area before matriculating at the University of California, Berkeley for undergraduate and graduate studies. At Berkeley he studied under Robert M. Solovay, producing a doctoral dissertation situated in set theory and recursion theory. During his formative years at Berkeley he interacted with contemporaries active in the broader logical community, including faculty and visitors associated with Harvard University, Massachusetts Institute of Technology, and the Institute for Advanced Study.

Mathematical career

Harrington held academic positions at several institutions, including the University of California, Berkeley and later appointments at institutions such as University of California, Los Angeles and Dartmouth College. Throughout his career he participated in seminars and summer schools organized by bodies like the American Mathematical Society and the Association for Symbolic Logic, and he presented at international venues including conferences hosted by the International Congress of Mathematicians, the European Set Theory Conference, and workshops at the University of Oxford and the University of Cambridge. His collaborations extended to researchers at the University of California, Irvine, the University of Chicago, and Princeton University.

Research contributions

Harrington made several foundational contributions across topics in set theory and recursion theory. He is widely known for work on determinacy: collaborating with Donald A. Martin and John R. Steel he helped elucidate connections between determinacy hypotheses and structural consequences in descriptive set theory, impacting analyses related to the Axiom of Determinacy and projective sets. Harrington's results tied determinacy statements to large cardinal assumptions studied in the context of measurable cardinal, Woodin cardinal, and strong cardinal hierarchies.

In partition calculus and combinatorial set theory, Harrington produced results that related partition relations for ordinals and cardinals to definability properties in effective descriptive set theory, drawing on methods also used by Paul Erdős and András Hajnal. His work on recursion theory and degrees of unsolvability connected classical themes from Alonzo Church and Alan Turing to modern priority arguments and hyperarithmetical hierarchies influenced by Gerald E. Sacks and Harvey Friedman.

Harrington also contributed to the development of inner model theory, where interactions between determinacy, iterable models, and fine structural analysis were pursued by researchers such as W. Hugh Woodin, John R. Steel, and Donald A. Martin. His insights informed later constructions of canonical inner models accommodating large cardinals and clarified whether certain regularity properties for sets of reals follow from large cardinal hypotheses. Additionally, Harrington's investigations touched on reverse mathematics and proof-theoretic strength, linking theorems about definable sets and games to subsystems studied by Stephen G. Simpson and others in the program pioneered by Harvey Friedman.

Awards and honors

Harrington's research earned recognition within the logical community, including invited addresses and lecture series at conferences organized by the Association for Symbolic Logic and the European Mathematical Society. He received research fellowships and visiting appointments at institutions such as the Institute for Advanced Study and national research centers supported by agencies like the National Science Foundation. His collaborations and publications have been cited by prizewinning work in set theory and by recipients of honors such as the Hausdorff Medal and the Sacks Prize awarded in related areas.

Selected publications

- Harrington, L.; Martin, D.A.; Steel, J.R., "Determinacy and definable determinacy", Annals of Mathematics style publications addressing determinacy and projective sets. - Harrington, L., Papers on partition relations and effective descriptive set theory in journals allied with the American Mathematical Society and the London Mathematical Society. - Harrington, L.; Solovay, R.M., Collaborative work from Berkeley era on set-theoretic constructions and recursion-theoretic consequences. - Harrington, L.; Sacks, G.E., Articles connecting recursively enumerable degrees and hyperarithmetical hierarchies. - Harrington, L., Selected lecture notes and survey articles presented at meetings of the Association for Symbolic Logic and summer schools at the Mathematical Sciences Research Institute.

Category:American mathematicians Category:Set theorists Category:Mathematical logicians