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Entscheidungsproblem
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== References == * {{Cite book |last1=Hilbert |first1=David |title=Grundzüge der theoretischen Logik |last2=Ackermann |first2=Wilhelm |publisher=[[Springer-Verlag]] |year=1928 |isbn=0821820249 |language=de |trans-title=Principles of mathematical logic |author-link=David Hilbert |author-link2=Wilhelm Ackermann}} * [[Alonzo Church]], "An unsolvable problem of [[elementary number theory]]", American Journal of Mathematics, 58 (1936), pp 345–363 * [[Alonzo Church]], "A note on the Entscheidungsproblem", Journal of Symbolic Logic, 1 (1936), pp 40–41. * {{Cite book |last=Davis |first=Martin |title=Engines of logic: mathematicians and the origin of the computer |date=2001 |publisher=Norton |isbn=978-0-393-32229-3 |edition=1. publ. as Norton paperback |series=Norton paperback |location=New York, NY London |author-link=Martin Davis (mathematician)}} * [[Alan Turing]], "[[On Computable Numbers, with an Application to the Entscheidungsproblem]]", Proceedings of the [[London Mathematical Society]], Series 2, 42 (1936–7), pp 230–265. Online versions: [https://wayback.archive-it.org/all/20171002211121/https://academic.oup.com/plms/article-abstract/s2-42/1/230/1491926/On-Computable-Numbers-with-an-Application-to-the?redirectedFrom=fulltext from journal website], [https://web.archive.org/web/20031007003709/http://www.turingarchive.org/browse.php/B/12 from Turing Digital Archive], [http://www.abelard.org/turpap2/tp2-ie.asp from abelard.org]. Errata appeared in Series 2, 43 (1937), pp 544–546. * [[Martin Davis (mathematician)|Davis, Martin]], "The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems And Computable Functions", Raven Press, New York, 1965. Turing's paper is #3 in this volume. Papers include those by Gödel, Church, Rosser, Kleene, and Post. * {{Cite book |last=Hodges |first=Andrew |title=Alan Turing: the enigma |title-link=Alan Turing: The Enigma |date=1983 |publisher=Simon and Schuster |isbn=978-0-671-49207-6 |location=New York |author-link=Andrew Hodges}} Biography of Alan M. Turing. Cf Chapter "The Spirit of Truth" for a history leading to, and a discussion of, his proof. * [[Robert Soare|Soare, Robert I.]], "Computability and recursion", Bull. Symbolic Logic 2 (1996), no. 3, 284–321. * [[Stephen Toulmin|Toulmin, Stephen]], "Fall of a Genius", a book review of "[[Alan Turing: The Enigma]] by Andrew Hodges", in The New York Review of Books, 19 January 1984, p. 3ff. * [[Alfred North Whitehead|Whitehead, Alfred North]]; [[Bertrand Russell|Russell, Bertrand]], Principia Mathematica to *56, Cambridge at the University Press, 1962. Re: the problem of paradoxes, the authors discuss the problem, that a set not be an object in any of its "determining functions", in particular "Introduction, Chap. 1 p. 24 "...difficulties which arise in formal logic", and Chap. 2.I. "The Vicious-Circle Principle" p. 37ff, and Chap. 2.VIII. "The Contradictions" p. 60 ff.
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