Donald A. Martin
Encyclopedia
Donald A. Martin (born 24 December 1940) is a set theorist and philosopher of mathematics at UCLA
, where he is a member of the faculty of mathematics and philosophy
.
Among Martin's most notable work are the proofs of analytic
determinacy
(from the existence of a measurable cardinal
), Borel
determinacy
(from ZFC alone), the proof (with John R. Steel
) of projective determinacy (from suitable large cardinal axioms), and his work on Martin's axiom
.
Martin is a Harvard junior fellow.
University of California, Los Angeles
The University of California, Los Angeles is a public research university located in the Westwood neighborhood of Los Angeles, California, USA. It was founded in 1919 as the "Southern Branch" of the University of California and is the second oldest of the ten campuses...
, where he is a member of the faculty of mathematics and philosophy
UCLA Department of Philosophy
The UCLA Department of Philosophy is a constituent department of the Division of Humanities in the UCLA College of Letters and Science. From the mid-20th century, the department has been a leading and widely respected center for the study of Analytic Philosophy, especially Mathematical Logic,...
.
Among Martin's most notable work are the proofs of analytic
Analytic set
In descriptive set theory, a subset of a Polish space X is an analytic set if it is a continuous image of a Polish space. These sets were first defined by and his student .- Definition :There are several equivalent definitions of analytic set...
determinacy
Determinacy
In set theory, a branch of mathematics, determinacy is the study of under what circumstances one or the other player of a game must have a winning strategy, and the consequences of the existence of such strategies.-Games:...
(from the existence of a measurable cardinal
Measurable cardinal
- Measurable :Formally, a measurable cardinal is an uncountable cardinal number κ such that there exists a κ-additive, non-trivial, 0-1-valued measure on the power set of κ...
), Borel
Borel set
In mathematics, a Borel set is any set in a topological space that can be formed from open sets through the operations of countable union, countable intersection, and relative complement...
determinacy
Determinacy
In set theory, a branch of mathematics, determinacy is the study of under what circumstances one or the other player of a game must have a winning strategy, and the consequences of the existence of such strategies.-Games:...
(from ZFC alone), the proof (with John R. Steel
John R. Steel
John Robert Steel is a set theorist at University of California, Berkeley . He has made many contributions to the theory of inner models and determinacy. With Donald A. Martin, he proved projective determinacy, assuming the existence of sufficient large cardinals. He earned his Ph.D...
) of projective determinacy (from suitable large cardinal axioms), and his work on Martin's axiom
Martin's axiom
In the mathematical field of set theory, Martin's axiom, introduced by , is a statement which is independent of the usual axioms of ZFC set theory. It is implied by the continuum hypothesis, so certainly consistent with ZFC, but is also known to be consistent with ZF + ¬ CH...
.
Martin is a Harvard junior fellow.