John Robert Steel (born October 30, 1948) is an American set theorist at University of California, Berkeley (formerly at UCLA). 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. in Logic & the Methodology of Science at Berkeley in 1977 under the joint supervision of John West Addison Jr. and Stephen G. Simpson. [1]
In 1988, the Association for Symbolic Logic awarded him, Donald A. Martin and W. Hugh Woodin the Karp Prize for their work on the consistency of determinacy relative to large cardinals. In 2015, the European Set Theory Society awarded him and Ronald Jensen the Hausdorff Medal for their paper "K without the measurable".
In 2012, Steel held the Gödel Lecture titled The hereditarily ordinal definable sets in models of determinacy.
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory — as a branch of mathematics — is mostly concerned with those that are relevant to mathematics as a whole.
In mathematics, the axiom of determinacy is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962. It refers to certain two-person topological games of length ω. AD states that every game of a certain type is determined; that is, one of the two players has a winning strategy.
In mathematical logic, projective determinacy is the special case of the axiom of determinacy applying only to projective sets.
Donald Anthony Martin, also known as Tony Martin, is an American set theorist and philosopher of mathematics at UCLA, where he is an emeritus professor of mathematics and philosophy.
William Hugh Woodin is an American mathematician and set theorist at Harvard University. He has made many notable contributions to the theory of inner models and determinacy. A type of large cardinals, the Woodin cardinals, bears his name. In 2023, he was elected to the National Academy of Sciences.
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 similarly, "determinacy" is the property of a game whereby such a strategy exists. Determinacy was introduced by Gale and Stewart in 1950, under the name "determinateness".
Robert Martin Solovay is an American mathematician working in set theory.
Steve Jackson is an American set theorist at the University of North Texas. Much of his most notable work has involved the descriptive set-theoretic consequences of the axiom of determinacy. In particular he is known for having calculated the values of all the projective ordinals under the assumption that the axiom of determinacy holds.
The Association for Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic. The ASL was founded in 1936, and its first president was Curt John Ducasse. The current president of the ASL is Phokion Kolaitis.
Ronald Björn Jensen is an American mathematician who lives in Germany, primarily known for his work in mathematical logic and set theory.
In the mathematical field of set theory, the proper forcing axiom (PFA) is a significant strengthening of Martin's axiom, where forcings with the countable chain condition (ccc) are replaced by proper forcings.
In descriptive set theory, a set is said to be homogeneously Suslin if it is the projection of a homogeneous tree. is said to be -homogeneously Suslin if it is the projection of a -homogeneous tree.
In set theory, Ω-logic is an infinitary logic and deductive system proposed by W. Hugh Woodin as part of an attempt to generalize the theory of determinacy of pointclasses to cover the structure . Just as the axiom of projective determinacy yields a canonical theory of , he sought to find axioms that would give a canonical theory for the larger structure. The theory he developed involves a controversial argument that the continuum hypothesis is false.
In descriptive set theory, the Borel determinacy theorem states that any Gale–Stewart game whose payoff set is a Borel set is determined, meaning that one of the two players will have a winning strategy for the game. A Gale–Stewart game is a possibly infinite two-player game, where both players have perfect information and no randomness is involved.
Benedikt Löwe is a German mathematician and logician working at the universities of Amsterdam, Hamburg, and Cambridge. He is known for his work on mathematical logic and the foundations of mathematics, as well as for initiating the interdisciplinary conference series Foundations of the Formal Sciences and Computability in Europe.
The Higher Infinite: Large Cardinals in Set Theory from their Beginnings is a monograph in set theory by Akihiro Kanamori, concerning the history and theory of large cardinals, infinite sets characterized by such strong properties that their existence cannot be proven in Zermelo–Fraenkel set theory (ZFC). This book was published in 1994 by Springer-Verlag in their series Perspectives in Mathematical Logic, with a second edition in 2003 in their Springer Monographs in Mathematics series, and a paperback reprint of the second edition in 2009 (ISBN 978-3-540-88866-6).
Itay Neeman is a set theorist working as a professor of mathematics at the University of California, Los Angeles. He has made major contributions to the theory of inner models, determinacy and forcing.
The Gödel Lecture is an honor in mathematical logic given by the Association for Symbolic Logic, associated with an annual lecture at the association's general meeting. The award is named after Kurt Gödel and has been given annually since 1990.
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