Donald A. Martin completed his Bachelor of Science at the Massachusetts Institute of Technology in 1962 before advancing the field of set theory through his research on determinacy. His career as a mathematician, philosopher, and university teacher has spanned decades at institutions including The Rockefeller University and the University of California, Los Angeles, where he remains a professor emeritus.
Contributions to Logic and Set Theory
The mathematical research conducted by Martin includes the proof of Borel determinacy using ZFC axioms and the proof of analytic determinacy, which requires the existence of a measurable cardinal. Working alongside John R. Steel, he provided a proof of projective determinacy predicated on suitable large cardinal axioms. His involvement in set theory further encompasses development of Martin's axiom.
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Within the specific field of recursion theory, Martin formulated a conjecture during the late 1970s concerning nontrivial definable Turing invariant functions. This hypothesis, which suggests such functions are limited to the Turing jump and its transfinite iterates, appeared as an entry in the Victoria Delfino problems, an appendix within the proceedings of the Caltech-UCLA Logic Seminar. The broader body of his work includes the Martin measure on Turing degrees and Martin's Conjecture.
Academic Appointments and Recognition
His professional tenure has been primarily linked to the University of California, Los Angeles, following his time at The Rockefeller University. His contributions to the mathematical community have been acknowledged through several honors, including the Carol Karp Prize in 1988, a Guggenheim Fellowship in 1989, and appointments as a Tarski lecturer in 1992 and a Gödel lecturer in 1994. He holds membership in the American Mathematical Society and the American Academy of Arts and Sciences, and he became a Fellow of the American Mathematical Society in 2014.
Fast facts
- Born: 1940
- Nationality: United States
- Educated at: Massachusetts Institute of Technology
- Primary fields: Set theory, mathematical logic
- Notable honor: Carol Karp Prize (1988)
- Professional status: Professor emeritus
Questions readers ask
What is the focus of Martin's conjecture?
It concerns recursion theory and posits that the only nontrivial definable Turing invariant functions are the Turing jump and its iterates.
Which major proofs is Donald A. Martin known for?
He is recognized for proofs of Borel determinacy, analytic determinacy, and, with John R. Steel, projective determinacy.
Achievements
- Carol Karp Prize — 1988
- Held posts at University of California, Los Angeles and The Rockefeller University
- Fields: set theory, mathematics and mathematical logic
