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Emil Leon Post (February 11 1897 Augustów Poland – April 21 1954 New York City) was an Polish mathematician and logician.
Early work Post was born into a Polish-Jewish family that immigrated to the USA when he was a child. After completing his Ph.D. in mathematics at Columbia University, he did a postdoc at Princeton University. While at Princeton, he came very close to discovering the incompleteness of Principia Mathematica, which Kurt Gödel proved 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 College of the College of the City of New York, where he remained until his death. In his Columbia University doctoral 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 Wittgenstein and Charles Peirce and 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. Recursion theory In 1936. Post developed, independently of Alan Turing's Turing machine model, an essentially equivalent 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 rewriting and developed by Post in the 1920s but first published in 1943). The unsolvability of his Post correspondence problem turned 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 Society in 1944, he raised the question of the existence of a uncomputable recursively enumerable set whose Turing degree is 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. Selected Papers Essential reading See also | ||||||||
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