Justin Tatch Moore (born 1974) [1] is a set theorist and logician. He is a full professor in mathematics at Cornell University.
Moore received his PhD in 2000 from the University of Toronto under the supervision of Stevo Todorcevic. [1] [2] He was an assistant professor in mathematics at Boise State University. In the fall of 2007, he joined the faculty at Cornell University.
His primary research area is Ramsey theory of infinite sets. He is known for solutions to the basis problem for uncountable linear orders and to the L space problem from general topology [3] and for his work in determining the consequences of relating the continuum to certain values of the aleph function. [4] Moore, together with his PhD student Yash Lodha, produced the first torsion-free counterexample to the von Neumann-Day problem, originally described by mathematician John von Neumann in 1929. Lodha presented this solution at the London Mathematical Society's Geometric and Cohomological Group Theory symposium in August 2013. [5]
Moore won the "Young Scholar's Competition" award in 2006, in Vienna, Austria. The Competition was a part of the "Horizons of Truth" celebrating the Gödel Centenary 2006. [6] He was an invited speaker at the ICM, Hyderabad 2010, Logic session, where he presented his solution to the problem of constructing an L-space. The L-space was constructed without assuming additional axioms and by combining Todorcevic's rho functions with number theory. [7] [8]
Moore is an editor for the Archive of Mathematical Logic where he handles papers in set theory. [4] He was one of the organizers of the fall 2012 Thematic Program in Forcing and its Applications (Forcing Axioms and their Applications) at the Fields Institute. [9] In 2012, he was elected as a Fellow (Inaugural Class of Fellows) of the American Mathematical Society. [10]
David Hilbert was a German mathematician and one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics.
John von Neumann was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. Von Neumann was generally regarded as the foremost mathematician of his time and said to be "the last representative of the great mathematicians". He integrated pure and applied sciences.
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.
Hilbert's fifth problem is the fifth mathematical problem from the problem list publicized in 1900 by mathematician David Hilbert, and concerns the characterization of Lie groups.
In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted by V, is the class of hereditary well-founded sets. This collection, which is formalized by Zermelo–Fraenkel set theory (ZFC), is often used to provide an interpretation or motivation of the axioms of ZFC. The concept is named after John von Neumann, although it was first published by Ernst Zermelo in 1930.
Hilbert's sixth problem is to axiomatize those branches of physics in which mathematics is prevalent. It occurs on the widely cited list of Hilbert's problems in mathematics that he presented in the year 1900. In its common English translation, the explicit statement reads:
In mathematics, the von Neumann conjecture stated that a group G is non-amenable if and only if G contains a subgroup that is a free group on two generators. The conjecture was disproved in 1980.
David Gale was an American mathematician and economist. He was a professor emeritus at the University of California, Berkeley, affiliated with the departments of mathematics, economics, and industrial engineering and operations research. He has contributed to the fields of mathematical economics, game theory, and convex analysis.
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 set theory, Ω-logic is an infinitary logic and deductive system proposed by W. Hugh Woodin (1999) 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 set theory, a branch of mathematical logic, Martin's maximum, introduced by Foreman, Magidor & Shelah (1988) and named after Donald Martin, is a generalization of the proper forcing axiom, itself a generalization of Martin's axiom. It represents the broadest class of forcings for which a forcing axiom is consistent.
András Hajnal was a professor of mathematics at Rutgers University and a member of the Hungarian Academy of Sciences known for his work in set theory and combinatorics.
Stevo Todorčević, is a Yugoslavian mathematician specializing in mathematical logic and set theory. He holds a Canada Research Chair in mathematics at the University of Toronto, and a director of research position at the Centre national de la recherche scientifique in Paris.
Michel Louis Balinski was an applied mathematician, economist, operations research analyst and political scientist. As a Polish-American, educated in the United States, he lived and worked primarily in the United States and France. He was known for his work in optimisation, convex polyhedra, stable matching, and the theory and practice of electoral systems, jury decision, and social choice. He was Directeur de Recherche de classe exceptionnelle (emeritus) of the C.N.R.S. at the École Polytechnique (Paris). He was awarded the John von Neumann Theory Prize by INFORMS in 2013.
In mathematics, iterated forcing is a method for constructing models of set theory by repeating Cohen's forcing method a transfinite number of times. Iterated forcing was introduced by Solovay and Tennenbaum (1971) in their construction of a model of set theory with no Suslin tree. They also showed that iterated forcing can construct models where Martin's axiom holds and the continuum is any given regular cardinal.
In the field of mathematics called set theory, the open coloring axiom is an axiom about coloring edges of a graph whose vertices are a subset of the real numbers: two different versions were introduced by Abraham, Rubin & Shelah (1985) and by Todorčević (1989). The open coloring axiom follows from the proper forcing axiom.
In mathematics, S-space is a regular topological space that is hereditarily separable but is not a Lindelöf space. L-space is a regular topological space that is hereditarily Lindelöf but not separable. A space is separable if it has a countable dense set and hereditarily separable if every subspace is separable.
(Ilse) Lisl Novak Gaal is an Austrian-born American mathematician known for her contributions to set theory and Galois theory. She was the first woman to hold a tenure-track position in mathematics at Cornell University, and is an associate professor emeritus at the University of Minnesota.
