Donald Anthony Martin (born December 24, 1940), also known as Tony Martin, is an American
set theorist and
philosopher of mathematics at
UCLA
The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California ...
, where he is an emeritus professor of mathematics and
philosophy.
Education and career
Martin received his B.S. from the
Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...
in 1962 and was a
Junior Fellow of the Harvard Society of Fellows in 1965–67. In 2014, he became a Fellow of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
.
List of Fellows of the American Mathematical Society
retrieved 2014-12-17
Philosophical and mathematical work
Among Martin's most notable works are the proofs of analytic determinacy
Determinacy is a subfield of set theory, a branch of mathematics, that examines the conditions under which one or the other player of a game has a winning strategy, and the consequences of the existence of such strategies. Alternatively and sim ...
(from the existence of a measurable cardinal
In mathematics, a measurable cardinal is a certain kind of large cardinal number. In order to define the concept, one introduces a two-valued measure on a cardinal , or more generally on any set. For a cardinal , it can be described as a subdivisi ...
), Borel determinacy
Determinacy is a subfield of set theory, a branch of mathematics, that examines the conditions under which one or the other player of a game has a winning strategy, and the consequences of the existence of such strategies. Alternatively and sim ...
(from ZFC alone), the proof (with John R. Steel) of projective determinacy In mathematical logic, projective determinacy is the special case of the axiom of determinacy applying only to projective sets.
The axiom of projective determinacy, abbreviated PD, states that for any two-player infinite game of perfect informatio ...
(from suitable large cardinal axioms), and his work on Martin's axiom
In the mathematical field of set theory, Martin's axiom, introduced by Donald A. Martin and Robert M. Solovay, is a statement that is independent of the usual axioms of ZFC set theory. It is implied by the continuum hypothesis, but it is consist ...
. The Martin measure on Turing degree
In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures the level of algorithmic unsolvability of the set.
Overview
The concept of Turing degree is fund ...
s is also named after Martin.
See also
* American philosophy
* List of American philosophers
This is a list of American philosophers; of philosophers who are either from, or spent many productive years of their lives in the United States.
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References
External links
*
List of publications
UCLA Logic center
Personal Website at UCLA
1940 births
Living people
20th-century American mathematicians
21st-century American mathematicians
American logicians
UCLA Philosophy
Philosophers of mathematics
Set theorists
Fellows of the American Mathematical Society
Gödel Lecturers
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