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Leon Henkin (19 April 1921–1 November 2006) was a logician at the University of California, Berkeley. He was principally known for the "Henkin Completeness Proof": his version of the proof of the semantic completeness of standard systems of first-order logic. [[Image: http://www.berkeley.edu/news/media/download/2006/11/henkin.jpg]] April 19 is the 109th day of the year in the Gregorian calendar (110th in leap years). ...
Year 1921 (MCMXXI) was a common year starting on Saturday (see link for full calendar). ...
November 1 is the 305th day of the year (306th in leap years) in the Gregorian Calendar, with 60 days remaining. ...
For the Manfred Mann album, see 2006 (album). ...
A logician is a philosopher, mathematician, or other whose topic of scholarly study is logic. ...
The University of California, Berkeley (also known as UC Berkeley, Berkeley, Cal, and by other names, see below) is the oldest and flagship campus of the ten-campus University of California system. ...
In mathematics and related technical fields, a mathematical object is complete if nothing needs to be added to it. ...
First-order logic (FOL) is a universal language in symbolic science, and is in use everyday by mathematicians, philosophers, linguists, computer scientists and practitioners of artificial intelligence. ...
The completeness proof
Henkin's result was not novel; it had first been proved by Kurt Gödel in his doctoral dissertation which was completed in 1929. (See Gödel's completeness theorem. Gödel published a version of the proof in 1930.) Henkin's 1949 proof is much easier to survey than Gödel's and has thus become the standard choice of completeness proof for presentation in introductory classes and texts. Kurt Gödel (IPA: ) (April 28, 1906 Brno, then Austria-Hungary, now Czech Republic – January 14, 1978 Princeton, New Jersey) was an Austrian logician, mathematician, and philosopher of mathematics One of the most significant logicians of all time, Gödels work has had immense impact upon scientific and philosophical...
Gödels completeness theorem is an important theorem in mathematical logic which was first proved by Kurt Gödel in 1929. ...
The proof is non-constructive (a pure existence proof): while it guarantees that if a sentence α follows (semantically) from a set of sentences Σ, then there is a proof of α from Σ, it gives no indication of the nature of that proof. In mathematics, an existence theorem is a theorem with a statement beginning there exist(s) .., or more generally for all x, y, ... there exist(s) .... That is, in more formal terms of symbolic logic, it is a theorem with a statement involving the existential quantifier. ...
Later, Henkin generalized this result to a variant of Church's higher-order logic. This variant uses general models (also called Henkin models): the higher types need not be interpreted by the full space of functions; a subset of the function space may be used instead. Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician and logician who was responsible for some of the foundations of theoretical computer science. ...
In mathematics, higher-order logic is distinguished from first-order logic in a number of ways. ...
Early life He was born in Brooklyn, into a Russian Jewish immigrant family. His first degree was in mathematics and philosophy from Columbia College, in 1941. He took a master's degree there in 1942. Brooklyn (named for the Dutch city Breukelen) is one of the five boroughs of New York City. ...
Columbia College is the main undergraduate college at Columbia University, situated on the universitys main campus of Morningside Heights in the Borough of Manhattan in the City of New York. ...
He then worked in the Signal Corps Radar Laboratory, Belmar, New Jersey. As participant in the Manhattan project, he worked on isotope diffusion, in New York, and Oak Ridge, Tennessee. Belmar is a borough located in Monmouth County, New Jersey. ...
The Manhattan Project resulted in the development of the first nuclear weapons, and the first-ever nuclear detonation, at the Trinity test of July 16, 1945. ...
Oak Ridge is an incorporated city in Anderson and Roane Counties in East Tennessee, about 25 miles northwest of Knoxville. ...
Academic career He was a doctoral student of Alonzo Church at Princeton University, receiving his Ph.D. in 1947. He became Professor of Mathematics at the University of California, Berkeley, where he had a position from 1953. He received the 1964 Chauvenet Prize for exposition.[3] He was a collaborator of Alfred Tarski, and an ally in promoting logic.[1] Princeton University is a coeducational private university located in Princeton, New Jersey, in the United States of America. ...
A professor giving a lecture The meaning of the word professor (Latin: one who claims publicly to be an expert) varies. ...
Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ...
The University of California, Berkeley (also known as UC Berkeley, Berkeley, Cal, and by other names, see below) is the oldest and flagship campus of the ten-campus University of California system. ...
The Chauvenet Prize, consisting of a prize of $1,000 and a certificate, is awarded yearly by the Mathematical Association of America in recognition of an outstanding expository article on a mathematical topic. ...
// Alfred Tarski (January 14, 1902, Warsaw, Russian-ruled Poland – October 26, 1983, Berkeley, California) was a logician and mathematician who spent four decades as a professor of mathematics at the University of California, Berkeley. ...
Awards received - 2000 - Leon Henkin Citation - for Distinguished Service, which is presented to a (UC) faculty member for "exceptional commitment to the educational development of students from groups who are underrepresented in the academy."
- 1991 - Berkeley Citation - the highest honor/award bestowed by the University of California
- 1990 - First recipient of the Gung and Hu Award for Distinguished Service to Mathematics
- 1972 - Lester R. Ford Award - for Mathematical foundations for mathematics, American Mathematical Monthly 78 (1971), 463-487.
- 1964 - The Chauvenet Prize, Mathematical Association of America award to the author of an outstanding expository article on a mathematical topic by a member of the Association.
Lester Randolph Ford, Sr. ...
The American Mathematical Monthly is a mathematical journal published 10 times each year by the Mathematical Association of America since 1894. ...
The Chauvenet Prize, consisting of a prize of $1,000 and a certificate, is awarded yearly by the Mathematical Association of America in recognition of an outstanding expository article on a mathematical topic. ...
See also In logic a branching quantifier is a partial ordering of quantifiers for Q∈{∀,∃}. In classical logic, quantifier prefixes are linearly ordered such that the value of a variable x bound by a quantifier Q depends on the value of the variables y1,...,yn bound by quantifiers Qy1,...,Qyn preceding Q...
References - Henkin, Leon. 1949. "The Completeness of the First-Order Functional Calculus", Journal of Symbolic Logic. 14: 159–166.
- Henkin, Leon. 1950. "Completeness in the theory of types", Journal of Symbolic Logic 15: 81–91.
Notes - ^ Solomon Feferman on Tarski's campaigning [1], [2] explains Henkin's role as recruit and ally.
Solomon Feferman is a mathematician and philosopher at Stanford University. ...
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