In set theory, the ground axiom was introduced by Hamkins (2005) and Reitz (2007). It states that the universe is not a nontrivial set forcing extension of an inner model.
In mathematics, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. It states:
There is no set whose cardinality is strictly between that of the integers and the real numbers.
Informally, a definable real number is a real number that can be uniquely specified by its description. The description may be expressed as a construction or as a formula of a formal language. For example, the positive square root of 2, , can be defined as the unique positive solution to the equation , and it can be constructed with a compass and straightedge.
In mathematics, an integer sequence is a sequence of integers.
Ralph Jasper Faudree was a mathematician, a professor of mathematics and the former provost of the University of Memphis.
In mathematics, an unfoldable cardinal is a certain kind of large cardinal number.
Nathan Jacobson was an American mathematician.
Irving Kaplansky was a mathematician, college professor, author, and musician.
Daniel J. Kleitman is an American mathematician and professor of applied mathematics at MIT. His research interests include combinatorics, graph theory, genomics, and operations research.
James Burton Ax was an American mathematician who proved several results in algebra and number theory by using model theory. He shared, with Simon B. Kochen, the seventh Frank Nelson Cole Prize in Number Theory, which was awarded for a series of three joint papers on Diophantine problems.
John Colin Stillwell is an Australian mathematician on the faculties of the University of San Francisco and Monash University.
In mathematics, the Bogomolov–Miyaoka–Yau inequality is the inequality
In set theory, a branch of mathematics, Kunen's inconsistency theorem, proved by Kenneth Kunen (1971), shows that several plausible large cardinal axioms are inconsistent with the axiom of choice.
In mathematics — specifically, in functional analysis — an Asplund space or strong differentiability space is a type of well-behaved Banach space. Asplund spaces were introduced in 1968 by the mathematician Edgar Asplund, who was interested in the Fréchet differentiability properties of Lipschitz functions on Banach spaces.
In algebra, the Amitsur–Levitzki theorem states that the algebra of n by n matrices satisfies a certain identity of degree 2n. It was proved by Amitsur and Levitsky (1950). In particular matrix rings are polynomial identity rings such that the smallest identity they satisfy has degree exactly 2n.
Joel David Hamkins is an American mathematician and philosopher based at the University of Oxford. He has made contributions in mathematical and philosophical logic, particularly set theory and the philosophy of set theory, in computability theory, and in group theory.
In mathematical set theory, a worldly cardinal is a cardinal κ such that the rank Vκ is a model of Zermelo–Fraenkel set theory.
In mathematics, the wholeness axiom is a strong axiom of set theory introduced by Paul Corazza in 2000.
Joan Bagaria Pigrau is a Catalan mathematician, logician and set theorist at ICREA and University of Barcelona. He has made many contributions concerning forcing, large cardinals, infinite combinatorics and their applications to other areas of mathematics. He earned his Ph.D. in Logic & the Methodology of Science at Berkeley in 1991 under the supervision of Haim Judah and W. Hugh Woodin. Since 2001, he has been ICREA Research Professor at University of Barcelona. He served as the first president of the European Set Theory Society (2007-11).
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).
Albert "Tommy" Wilansky was a Canadian-American mathematician, known for introducing Smith numbers.
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