Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
Gábor Szegő was a Hungarian-American mathematician. He was one of the foremost mathematical analysts of his generation and made fundamental contributions to the theory of orthogonal polynomials and Toeplitz matrices building on the work of his contemporary Otto Toeplitz.
In mathematics, extendible cardinals are large cardinals introduced by Reinhardt (1974), who was partly motivated by reflection principles. Intuitively, such a cardinal represents a point beyond which initial pieces of the universe of sets start to look similar, in the sense that each is elementarily embeddable into a later one.
Matthew Dean Foreman is an American mathematician at University of California, Irvine. He has made notable contributions in set theory and in ergodic theory.
In mathematics, Vopěnka's principle is a large cardinal axiom. The intuition behind the axiom is that the set-theoretical universe is so large that in every proper class, some members are similar to others, with this similarity formalized through elementary embeddings.
Robert Steinberg was a mathematician at the University of California, Los Angeles.
In Zermelo–Fraenkel set theory without the axiom of choice a strong partition cardinal is an uncountable well-ordered cardinal such that every partition of the set of size subsets of into less than pieces has a homogeneous set of size .
Richard Joseph Laver was an American mathematician, working in set theory.
In set theory, a branch of mathematics, Kunen's inconsistency theorem, proved by Kenneth Kunen, shows that several plausible large cardinal axioms are inconsistent with the axiom of choice.
John Charles Chenoweth McKinsey, usually cited as J. C. C. McKinsey, was an American mathematician known for his work on game theory and mathematical logic, particularly, modal logic.
James Andrew Clarkson was an American mathematician and professor of mathematics who specialized in number theory. He is known for proving inequalities in Hölder spaces, and derived from them, the uniform convexity of Lp spaces. His proofs are known in mathematics as Clarkson's inequalities. He was an operations' analyst during World War II, and was awarded the Medal of Freedom for his achievements. He wrote First reader on game theory, and many of his academic papers have been published in several scientific journals. He was an invited speaker at the 1932 International Congress of Mathematicians (ICM) in Zürich.
Joel David Hamkins is an American mathematician and philosopher who is O'Hara Professor of Philosophy and Mathematics at the University of Notre Dame. He has made contributions in mathematical and philosophical logic, set theory and philosophy of set theory, in computability theory, and in group theory.
James Michael Gardner Fell was a Canadian-American mathematician, specializing in functional analysis and representation theory. He is known for Fell bundles. He was an accomplished linguist who knew Sanskrit, Icelandic, German, French, Russian, Greek, and Latin.
Edward "Ted" Wilfred Odell, Jr. was an American mathematician, specializing in the theory of Banach spaces.
Bertram John Walsh is an American mathematician, specializing in locally convex spaces, harmonic analysis, and partial differential equations.
Roger David Nussbaum is an American mathematician, specializing in nonlinear functional analysis and differential equations.
Albert "Tommy" Wilansky was a Canadian-American mathematician, known for introducing Smith numbers.
Alexander "Sandy" Munro Davie is a Scottish mathematician and was the chess champion of Scotland in 1964, 1966, and 1969.
The term weak continuum hypothesis can be used to refer to the hypothesis that , which is the negation of the second continuum hypothesis. It is equivalent to a weak form of ◊ on . F. Burton Jones proved that if it is true, then every separable normal Moore space is metrizable.
