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Godel's Incompleteness TheoremsOxford University Press USA. 1992.An introduction to the work of the mathematical logician Kurt Godel, which guides the reader through his Theorem of Undecidability and his theories on the completeness of logic, the incompleteness of numbers and the consistency of the axiom of choice.
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12A beginner's guide to mathematical logicDover Publications. 2014.Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems. Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompletenes…Read more
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8Gödel's Incompleteness TheoremsIn Lou Goble (ed.), The Blackwell Guide to Philosophical Logic, Blackwell. 2017.At the turn of the century, there appeared two comprehensive mathematical systems, which were indeed so vast that it was taken for granted that all mathematics could be decided on the basis of them. However, in 1931, Kurt Gödel surprised the entire mathematical world with his epoch‐making paper which begins with the following startling words: The development of mathematics in the direction of greater precision has led to large areas of it being formalized, so that proofs can be carried out accor…Read more
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8A beginner's further guide to mathematical logicWorld Scientific. 2017.More on propositional and first-order logic -- More on propositional logic -- More on first-order logic -- Recursion theory and metamathematics -- Some special topics -- Elementary formal systems and recursive enumerability -- Some recursion theory -- Doubling up -- Metamathematical applications -- Elements of combinatory logic -- Beginning combinatory logic -- Combinatorics galore -- Sages, oracles, and doublets -- Complete and partial systems -- Combinators, recursion, and the undecidable -- W…Read more
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10Theory of Formal SystemsPrinceton University Press. 1961.This book serves both as a completely self-contained introduction and as an exposition of new results in the field of recursive function theory and its application to formal systems.
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20J. R. Shoenfield. Undecidable and creative theories. Fundamenta mathematicae, vol. 49 no. 2 , pp. 171–179Journal of Symbolic Logic 32 (1): 123. 1967.
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13Vladeta Vučković. Mathematics of incompleteness and undecidability. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 13 , pp. 123–150 (review)Journal of Symbolic Logic 37 (1): 195-196. 1972.
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24Rudy Rucker. Mind tools. The five levels of mathematical reality. Houghton Mifflin Company, Boston1987, viii + 328 pp (review)Journal of Symbolic Logic 53 (4): 1254-1255. 1988.
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10Exact Separation of Recursively Enumerable Sets Within TheoriesJournal of Symbolic Logic 25 (4): 362-362. 1960.
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72Some new double induction and superinduction principlesStudia Logica 49 (1). 1990.Some new double analogues of induction and transfinite recursion are given which yields a relatively simple proof of a result of Robert Cowen, [2] which in turn is a strengthening of an earlier result of Smullyan [1], which in turn gives a unified approach to Zorn's Lemma, the transfinite recursion theorem and certain results about ordinal numbers.
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45Undecidability and recursive inseparabilityZeitschrift fur mathematische Logik und Grundlagen der Mathematik 4 (7-11): 143-147. 1958.
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5Five Thousand B.C. and Other Philosophical FantasiesMacmillan. 1983.A collection of paradoxes, dialogues, problems, and essays discusses aspects of philosophy, including the natures of reality, truth, existence, and death.
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6This Book Needs No Title: A Budget of Living ParadoxesPrentice-Hall. 1980.Eighty paradoxes, logical lobyrinths, and intriguing enigmas progress from light fables and fancies to challenging Zen exercises and a novella and probe the timeless questions of philosophy and life.
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20Reviews. Evert W. Beth. The foundations of mathematics, A study in the philosophy of science. Studies in logic and the foundations of mathematics, North-Holland Publishing Company, Amsterdam 1959, XXVI + 741 pp (review)Journal of Symbolic Logic 27 (1): 73-75. 1962.
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1Review: J. R. Shoenfield, Undecidable and Creative Theories (review)Journal of Symbolic Logic 32 (1): 123-123. 1967.
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14An Isomorphism Related to Gödel's Fundamental OperationsLogic Journal of the IGPL 12 (6): 439-445. 2004.
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35Set theory and the continuum problemClarendon Press. 1996.A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.
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17Mind Tools. The Five Levels of Mathematical RealityJournal of Symbolic Logic 53 (4): 1254. 1988.
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20Forever undecided: a puzzle guide to GödelOxford University Press. 1987.Collects a variety of mathematics and logic puzzles, some based on the theorems of the mathematician Kurt Godel
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48Uniform Gentzen systemsJournal of Symbolic Logic 33 (4): 549-559. 1968.Generally speaking, it appears correct to say that in a formulation of first order logic in which a large number of connectives are taken as primitive which allows us to have our cake and eat it too.