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

(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.

References

External links

*
List of publicationsUCLA Logic centerPersonal 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 {{US-mathematician-stub

Education and career

Philosophical and mathematical work

See also

References

External links