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W. Hugh Woodin
William Hugh Woodin (born April 23, 1955) 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, bear his name. Biography Born in Tucson, Arizona, Woodin earned his Ph.D. from the University of California, Berkeley in 1984 under Robert M. Solovay. His dissertation title was ''Discontinuous Homomorphisms of C''(''Omega'') ''and Set Theory''. He served as chair of the Berkeley mathematics department for the 2002–2003 academic year. Woodin is a managing editor of the ''Journal of Mathematical Logic''. He was elected a Fellow of the American Academy of Arts and Sciences in 2000. He is the great-grandson of William Hartman Woodin, former Secretary of the Treasury. Work He has done work on the theory of generic multiverses and the related concept of Ω-logic, which suggested an argument that the continuum hypothesis is either undecid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tucson, Arizona
, "(at the) base of the black ill , nicknames = "The Old Pueblo", "Optics Valley", "America's biggest small town" , image_map = , mapsize = 260px , map_caption = Interactive map outlining Tucson , image_map1 = File:Pima County Incorporated and Unincorporated areas Tucson highlighted.svg , mapsize1 = 250px , map_caption1 = Location within Pima County , pushpin_label = Tucson , pushpin_map = USA Arizona#USA , pushpin_map_caption = Location within Arizona##Location within the United States , subdivision_type = Country , subdivision_type1 = State , subdivision_type2 = County , subdivision_name = United States , subdivision_name1 = Arizona , subdivision_name2 = Pima , established_title = Founded , established_date = August 20, 1775 , established_title1 = Incorporated , e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Mathematical Logic
The ''Journal of Mathematical Logic'' was established in 2001 and is published by World Scientific. It covers the field of mathematical logic and its applications. Abstracting and indexing The journal is abstracted and indexed in: * Current Mathematical Publications * Mathematical Reviews * MathSciNet * Zentralblatt MATH * Science Citation Index Expanded * Current Contents/Physical, Chemical and Earth Sciences * Journal Citation Reports ''Journal Citation Reports'' (''JCR'') is an annual publicationby Clarivate Analytics (previously the intellectual property of Thomson Reuters). It has been integrated with the Web of Science and is accessed from the Web of Science-Core Collect .../Science Edition External links * English-language journals Publications established in 2001 Mathematics journals World Scientific academic journals Logic journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Logicians
American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, people who self-identify their ancestry as "American" ** American English, the set of varieties of the English language native to the United States ** Native Americans in the United States, indigenous peoples of the United States * American, something of, from, or related to the Americas, also known as "America" ** Indigenous peoples of the Americas * American (word), for analysis and history of the meanings in various contexts Organizations * American Airlines, U.S.-based airline headquartered in Fort Worth, Texas * American Athletic Conference, an American college athletic conference * American Recordings (record label), a record label previously known as Def American * American University, in Washington, D.C. Sports teams Soccer * B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Symbolic Logic
The '' Journal of Symbolic Logic'' is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic. It was established in 1936 and covers mathematical logic. The journal is indexed by '' Mathematical Reviews'', Zentralblatt MATH, and Scopus. Its 2009 MCQ was 0.28, and its 2009 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as ... was 0.631. External links * Mathematics journals Publications established in 1936 Multilingual journals Quarterly journals Association for Symbolic Logic academic journals Logic journals Cambridge University Press academic journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Koellner
Peter Koellner is Professor of Philosophy at Harvard University. He received his Ph.D from MIT in 2003. His main areas of research are mathematical logic, specifically set theory, and philosophy of mathematics, philosophy of physics, analytic philosophy, and philosophy of language. In 2008 Koellner was awarded a Kurt Gödel Centenary Research Prize Fellowship. Currently, Koellner serves on the American Philosophical Association's Advisory Committee to the Eastern Division Program Committee in the area of Logic. According to a review by Pierre Matet on Zentralblatt MATH, his joint paper with Hugh Woodin ''Incompatible Ω-Complete Theories'' contains an illuminating discussion of the issues involved, which makes it recommended reading for anyone interested in modern set theory. Papers On the Question of Absolute Undecidability ''Philosophia Mathematica'' (III) 14 (2006) *On Reflection Principles, '' Annals of Pure and Applied Logic'', Volume 157, Issues 2-3, February 2009, Pages 20 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gödel Lecture
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. Award winners The list of award winners and lecture titles is maintained online by the Association for Symbolic Logic. * 1990 Ronald Jensen, ''Inner Models and Large Cardinals.'' * 1991 Dana Scott, ''Will Logicians be Replaced by Machines?'' * 1992 Joseph R. Shoenfield, ''The Priority Method.'' * 1993 Angus Macintyre, ''Logic of Real and p-adic Analysis: Achievements and Challenges.'' * 1994 Donald A. Martin, ''L(R): A Survey.'' * 1995 Leo Harrington, ''Gödel, Heidegger, and Direct Perception (or, Why I am a Recursion Theorist).'' * 1996 Saharon Shelah, ''Categoricity without compactness.'' * 1997 Solomon Feferman, ''Occupations and Preoccupations with Gödel: His *Works* and the Work.'' * 1998 Alexander S. Kechris, ''Current T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quanta Magazine
''Quanta Magazine'' is an editorially independent online publication of the Simons Foundation covering developments in physics, mathematics, biology and computer science. ''Undark Magazine'' described ''Quanta Magazine'' as "highly regarded for its masterful coverage of complex topics in science and math." The science news aggregator ''RealClearScience'' ranked ''Quanta Magazine'' first on its list of "The Top 10 Websites for Science in 2018." In 2020, the magazine received a National Magazine Award for General Excellence from the American Society of Magazine Editors for its "willingness to tackle some of the toughest and most difficult topics in science and math in a language that is accessible to the lay reader without condescension or oversimplification." The articles in the magazine are freely available to read online. ''Scientific American'', ''Wired'', ''The Atlantic'', and ''The Washington Post'', as well as international science publications like ''Spektrum der Wissensch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructible Universe
In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by , is a particular class of sets that can be described entirely in terms of simpler sets. is the union of the constructible hierarchy . It was introduced by Kurt Gödel in his 1938 paper "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis". In this paper, he proved that the constructible universe is an inner model of ZF set theory (that is, of Zermelo–Fraenkel set theory with the axiom of choice excluded), and also that the axiom of choice and the generalized continuum hypothesis are true in the constructible universe. This shows that both propositions are consistent with the basic axioms of set theory, if ZF itself is consistent. Since many other theorems only hold in systems in which one or both of the propositions is true, their consistency is an important result. What is can be thought of as being built in "stages" resembling the constr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth Value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (''true'' or '' false''). Computing In some programming languages, any expression can be evaluated in a context that expects a Boolean data type. Typically (though this varies by programming language) expressions like the number zero, the empty string, empty lists, and null evaluate to false, and strings with content (like "abc"), other numbers, and objects evaluate to true. Sometimes these classes of expressions are called "truthy" and "falsy" / "false". Classical logic In classical logic, with its intended semantics, the truth values are ''true'' (denoted by ''1'' or the verum ⊤), and '' untrue'' or '' false'' (denoted by ''0'' or the falsum ⊥); that is, classical logic is a two-valued logic. This set of two values is also called the Boolean domain. Corresponding semantics of l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Platonism
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts. The philosophy of mathematics has two major themes: mathematical realism and mathematical anti-realism. History The origin of mathematics is subject to arguments and disagreements. Whether the birth of mathematics was a random happening or induced by necessity during the development of other subjects, like physics, is still a matter of prolific debates. Many thinkers have contributed their ideas concerning the nature of mathematics. Today, some philosophers of mathematics aim to give accounts of this form of inquiry and its products as they stand, while others emphasize a role for themselves that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Hypothesis
In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that or equivalently, that In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this is equivalent to the following equation in aleph numbers: 2^=\aleph_1, or even shorter with beth numbers: \beth_1 = \aleph_1. The continuum hypothesis was advanced by Georg Cantor in 1878, and establishing its truth or falsehood is the first of Hilbert's 23 problems presented in 1900. The answer to this problem is independent of ZFC, so that either the continuum hypothesis or its negation can be added as an axiom to ZFC set theory, with the resulting theory being consistent if and only if ZFC is consistent. This independence was proved in 1963 by Paul Cohen, complementing earlier work by Kurt Gödel in 1940. The name of the hypothesis comes from the term '' the continuum'' for the real numbers. History Cantor believed the continuum hypothesis to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ω-logic
In set theory, Ω-logic is an infinitary logic and deductive system proposed by as part of an attempt to generalize the theory of determinacy of pointclasses to cover the structure H_. Just as the axiom of projective determinacy yields a canonical theory of H_, 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. Analysis Woodin's Ω-conjecture asserts that if there is a proper class of Woodin cardinals (for technical reasons, most results in the theory are most easily stated under this assumption), then Ω-logic satisfies an analogue of the completeness theorem. From this conjecture, it can be shown that, if there is any single axiom which is comprehensive over H_ (in Ω-logic), it must imply that the continuum is not \aleph_1. Woodin also isolated a specific axiom, a variation of Martin's maximum, which states that any Ω-consistent \Pi_2 (over H_) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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