Gödel logic is named after a mathematician with what nationality?
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Gödel logic In mathematical logic, a first-order Gödel logic is a member of a family of finite- or infinite-valued logics in which the sets of truth values "V" are closed subsets of the interval [0,1] containing both 0 and 1. Different such sets "V" in general determine different Gödel logics. The concept is named after Kurt Gödel.
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Kurt Gödel Kurt Friedrich Gödel ( , ; ] ; April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher. Considered along with Aristotle, Alfred Tarski and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, Alfred North Whitehead, and David Hilbert were analyzing the use of logic and set theory to understand the foundations of mathematics pioneered by Georg Cantor.
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Löb's theorem In mathematical logic, Löb's theorem states that in any formal system F with Peano arithmetic (PA), for any formula "P", if it is provable in F that "if "P" is provable in F then "P" is true", then "P" is provable in F. More formally, if "Bew(#P)" means that the formula "P" with Gödel number #"P" is provable (from the German "beweisbar"), then
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John Lemmon Edward John Lemmon (1 June 1930 – 29 July 1966) was a logician and philosopher born in Sheffield, England. He is most well known for his work on modal logic, particularly his joint text with Dana Scott published posthumously (Lemmon and Scott, 1977).
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Frege's theorem In metalogic and metamathematics, Frege's theorem is a metatheorem that states that the Peano axioms of arithmetic can be derived in second-order logic from Hume's principle. It was first proven, informally, by Gottlob Frege in his "Die Grundlagen der Arithmetik" ("The Foundations of Arithmetic"), published in 1884, and proven more formally in his "Grundgesetze der Arithmetik" ("The Basic Laws of Arithmetic"), published in two volumes, in 1893 and 1903. The theorem was re-discovered by Crispin Wright in the early 1980s and has since been the focus of significant work. It is at the core of the philosophy of mathematics known as neo-logicism.
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Alfred Horn Alfred Horn (February 17, 1918 – April 16, 2001) was an American mathematician notable for his work in lattice theory and universal algebra. His 1951 paper "On sentences which are true of direct unions of algebras" described Horn clauses and Horn sentences, which later would form the foundation of logic programming.
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Dugald Macpherson H. Dugald Macpherson is a mathematician and logician. He is Professor of Pure Mathematics at the University of Leeds.
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Gerhard Ringel Gerhard Ringel (October 28, 1919, in Kollnbrunn, Austria – June 24, 2008, in Santa Cruz, California) was a German mathematician who earned his Ph.D. from the University of Bonn in 1951. He was one of the pioneers in graph theory and contributed significantly to the proof of the Heawood conjecture (now the Ringel-Youngs theorem), a mathematical problem closely linked with the Four Color Theorem.
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Ronald Graham Ronald Lewis "Ron" Graham (born October 31, 1935) is a mathematician credited by the American Mathematical Society as being "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He has done important work in scheduling theory, computational geometry, Ramsey theory, and quasi-randomness.
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Giulio Giorello Giulio Giorello (] ; born 14 May 1945, Milan) is an Italian philosopher, mathematician, and epistemologist.
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Hao Wang (academic) Hao Wang (; 20 May 1921 – 13 May 1995) was a logician, philosopher, mathematician, and commentator on Kurt Gödel.
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Paul Bernays Paul Isaac Bernays (17 October 1888 – 18 September 1977) was a Swiss mathematician, who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant and close collaborator of David Hilbert.
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Harold Edwards (mathematician) Harold Mortimer Edwards, Jr. (born August 6, 1936) is an American mathematician working in number theory, algebra, and the history and philosophy of mathematics.
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Augustin-Louis Cauchy Baron Augustin-Louis Cauchy FRS FRSE (] ; 21 August 1789 – 23 May 1857) was a French mathematician and physicist who made pioneering contributions to analysis. He was one of the first to state and prove theorems of calculus rigorously, rejecting the heuristic principle of the generality of algebra of earlier authors. He almost singlehandedly founded complex analysis and the study of permutation groups in abstract algebra. A profound mathematician, Cauchy had a great influence over his contemporaries and successors. His writings range widely in mathematics and mathematical physics.
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David Hilbert David Hilbert (] ; 23 January 1862 – 14 February 1943) was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
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Errett Bishop Errett Albert Bishop (July 14, 1928 – April 14, 1983) was an American mathematician known for his work on analysis. He expanded constructive analysis in his 1967 "Foundations of Constructive Analysis", where he proved most of the important theorems in real analysis by constructive methods.
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Pierre de Fermat Pierre de Fermat (] ; (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the "Parlement" of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' "Arithmetica".
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William Kneale William Calvert Kneale (22 June 1906 – 24 June 1990) was an English logician best known for his 1962 book "The Development of Logic", a history of logic from its beginnings in Ancient Greece written with his wife Martha. Kneale was also known as a philosopher of science and the author of a book on probability and induction. Educated at the Liverpool Institute High School for boys, he later became a Fellow of Exeter College, Oxford, and in 1960 succeeded to the White's Professor of Moral Philosophy previously occupied by the linguistic philosopher J. L. Austin. He retired in 1966.
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David G. Cantor David Geoffrey Cantor (1935 – November 19, 2012) was an American mathematician, specializing in number theory and combinatorics. The Cantor–Zassenhaus algorithm for factoring polynomials is named after him; he and Hans Zassenhaus published it in 1981.
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Augustus De Morgan Augustus De Morgan ( ; 27 June 1806 – 18 March 1871) was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous.
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Joel David Hamkins Joel David Hamkins is an American mathematician and philosopher based at the City University of New York. 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.
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V. Frederick Rickey V. Frederick Rickey (born 17 December 1941) is an American logician and historian of mathematics.