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Encyclopedia > Donald A. Martin

Donald A. (Tony) Martin is a set theorist and philosopher of mathematics at UCLA. Among his most notable work are the proofs of 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. He is also Director of The UCLA Logic Center, which was established in the Fall of 2004. The University of California, Los Angeles, popularly known as UCLA, is a public, coeducational university situated in the neighborhood of Westwood within the city of Los Angeles. ... In mathematics, the Borel algebra (or Borel σ-algebra) on a topological space is either of two σ-algebras on a topological space X: The minimal σ-algebra containing the open sets. ... In mathematics, the axiom of determinacy (abbreviated as AD) is an axiom in set theory. ... The Zermelo-Fraenkel axioms of set theory (ZF) are the standard axioms of axiomatic set theory on which, together with the axiom of choice, all of ordinary mathematics is based in modern formulations. ... In mathematical logic, projective determinacy is the special case of the axiom of determinacy applying only to projective sets. ... In mathematics, a cardinal is called a large cardinal if it belongs to a class of cardinals, the existence of which provably cannot be proved within the standard axiomatic set theory ZFC, if one assumes ZFC itself is consistent. ... In axiomatic set theory, Martins axiom is a statement which is independent of the usual axioms of ZFC Set Theory. ...

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