- Emil Leon Post
name = Emil Leon Post
February 11, 1897
Augustów, then Russian Empire
April 21 1954,
New York City, flagicon|USA U.S.
known_for = Formulation 1,
Post correspondence problem, completeness-proof of Principia's propositional calculus
Emil Leon Post,
Ph.D., ( February 11 1897, Augustów– April 21 1954, New York City) was a mathematicianand logician.
Post was born into a Polish-Jewish family that immigrated to America when he was a child. After completing his Ph.D. in mathematics at
Columbia University, he did a post doctorate at Princeton University. While at Princeton, he came very close to discovering the incompleteness of " Principia Mathematica", which Kurt Gödelproved in 1931. Post then became a high school mathematics teacher in New York City. In 1936, he was appointed to the mathematics department at the City Collegeof the College of the City of New York, where he remained until his death.
Columbia Universitydoctoral thesis, Post proved, among other things, that the propositional calculus of "Principia Mathematica" was complete: all tautologies are theorems, given the "Principia" axioms and the rules of substitution and modus ponens. Post also devised truth tables independently of Wittgensteinand Charles Peirceand put them to good mathematical use. Jean Van Heijenoort's (1966) well-known source book on mathematical logic reprinted Post's classic article setting out these results.
In 1936. Post developed, independently of
Alan Turing, a mathematical model of computation that was essentially equivalent to the Turing machine model. Intending this as the first of a series of models of equivalent power but increasing complexity, he titled his paper Formulation 1. (This model is sometimes called "Post's machine" or a Post-Turing machine, but is not to be confused with Post's tag machines or other special kinds of Post canonical system, a computational model using string rewritingand developed by Post in the 1920s but first published in 1943).
The unsolvability of his
Post correspondence problemturned out to be exactly what was needed to obtain unsolvability results in the theory of formal languages.
In an influential address to the
American Mathematical Societyin 1944, he raised the question of the existence of an uncomputable recursively enumerableset whose Turing degreeis less than that of the halting problem. This question, which became known as Post's Problem, stimulated much research. It was solved in the affirmative in the 1950s by the introduction of the powerful priority method in recursion theory.
* 1936, "Finite Combinatory Processes - Formulation 1," "Journal of Symbolic Logic 1": 103-105.
* 1943, "Formal Reductions of the General Combinatorial Decision Problem," "
American Journal of Mathematics65": 197-215.
* 1944, "Recursively enumerable sets of positive integers and their decision problems," "
Bulletin of the American Mathematical Society50": 284-316. Introduces the important concept of many-one reduction.
* [http://www.amphilsoc.org/library/mole/p/post.htm Emil Leon Post Papers 1888-1995] -
American Philosophical Society, Philadelphia, Pennsylvania.
*Davis, Martin (1993). "The Undecidable" (Ed.), pp. 288-406. Dover. ISBN 0-486-43228-9. Reprints several papers by Post.
*Davis, Martin (1994). "Emil L. Post: His Life and Work" in Davis, M., ed., "Solvability, Provability, Definability: The Collected Works of Emil L. Post". Birkhäuser: xi--xxviii. A biographical essay.
Post's inversion formula
* [http://www.ams.org/notices/200805/ An interview with
Martin Davis] - Notices of the AMS, May 2008. Much material on Emil Post from his first-hand recollections.
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