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[Collection of important papers in mathematical logic]: 1. Alonzo Church: A note on the Entscheidungsproblem. + 2. Alonzo Church: Review of "On computable numbers, ...". + 3. Alan Turing: Computability and lambda-definability. 4. Emil Post: Finite combinatory processes-formulation I.
The Association for Symbolic Logic, 1936-1938. Royal8vo. In: Journal of Symbolic Logic, Volume 1-3. The three entire volumes bound in one offered here. Contemporary full cloth with silver gilt spine lettering. Provenance: Exlibris from the Rockefeller Institute for Medical Research, New York. A fine and completely clean copy.. All first editions. First paper: Church's paper, submitted on April 15, 1936, was the first to contain a demonstration that David Hilbert's 'Entscheidungsproblem' - i.e., the question as to whether there exists in mathematics a definite method of guaranteeing the truth or falsity of any mathematical statement - was unsolvable. Church did so by devising the 'lambda-calculus'. Church had earlier shown the existence of an unsolvable problem of elementary number theory, but his 1936 paper was the first to put his findings into the exact form of an answer to Hilbert's 'Entscheidungsproblem'. Church's paper bears on the question of what is computable, a problem addressed more directly by Alan Turing in his paper 'On computable numbers' published a few months later. The notion of an 'effective' or 'mechanical' computation in logic and mathematics became known as the Church-Turing thesis. (Hook & Norman: Origins of Cyberspace, 250).Second paper: Church coined the phrase 'Turing machine' in this review of Turing's paper 'On computable numbers'. With regard to Turing's proof of the insolvability of Hilbert's 'Entscheidungsproblem', Church acknowledged that "computability by a Turing machine ... has the advantage of making the identification with effectiveness in the ordinary (not explicitly defined) sense evident immediately - i.e. without the necessity of proving preliminary theorems". (Hook & Norman: Origins of Cyberspace, 251).Third paper: In this paper Turing first completed the cycle of proving that his 'computable functions', Church's 'lambda-definable functions', the and the 'general recursive functions', developed by Herbrand, Gödel and Kleene, are all identical. (Hook & Norman: Origins of Cyberspace, 395).Fourth paper: The Polish-American mathematician Emil Post made notable contributions to the theory of recursive functions. In the 1930s, independently of Turing, Post came up with the concept of a logic automaton similar to a Turing machine, which he described in the present paper (received on October 7, 1936). Post's paper was intended to fill a conceptual gap in Alonzo Church's paper on 'An unsolvable problem of elementary number theory'. Church had answered in the negative Hilbert's 'Entscheidungsproblem' but failed to provide the assertion that any such definitive method could be expressed as a formula in Church's lambda-calculus. Post proposed that a definite method would be one written in the form of instructions to mind-less worker operating on an infinite line of 'boxes' (equivalent to the Turing machines 'tape'). The range of instructions proposed by Post corresponds exactly to those performed by a Turing machine, and Church, who edited the Journal of Symbolic Logic, felt it necessary to insert an editorial note referring to Turing's "shortly forthcoming" paper on computable numbers, and asserting that "the present article ... although bearing a later date, was written entirely independently of Turing's". (Hook & Norman: Origins of Cyberspace, 356).Hook & Norman: Origins of Cyberspace, no. 250, 251,395,356
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