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5A 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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7Gödel'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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3A 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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15J. 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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11Vladeta 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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22Rudy 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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5Exact Separation of Recursively Enumerable Sets Within TheoriesJournal of Symbolic Logic 25 (4): 362-362. 1960.
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13Mind Tools. The Five Levels of Mathematical RealityJournal of Symbolic Logic 53 (4): 1254. 1988.
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15Forever 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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29Uniform 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.
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7An entertaining series of logic problems and puzzles of increasing difficulty, and all relating important mathematical and logical concepts, includes mind-benders, paradoxes, metapuzzles, number exercises, and a mathematical novel.
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58Recursion theory for metamathematicsOxford University Press. 1993.This work is a sequel to the author's Godel's Incompleteness Theorems, though it can be read independently by anyone familiar with Godel's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
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28Monadic Elementary Formal SystemsZeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (6): 81-83. 1961.
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32The tao is silentHarperSanFrancisco. 1977.The Tao Is Silent Is Raymond Smullyan's beguiling and whimsical guide to the meaning and value of eastern philosophy to westerners. "To me," Writes Smullyan, "Taoism means a state of inner serenity combined with an intense aesthetic awareness. Neither alone is adequate; a purely passive serenity is kind of dull, and an anxiety-ridden awareness is not very appealing." This is more than a book on Chinese philosophy. It is a series of ideas inspired by Taoism that treats a wide variety of subjects …Read more
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91Some unifying fixed point principlesStudia Logica 50 (1). 1991.This article is written for both the general mathematican and the specialist in mathematical logic. No prior knowledge of metamathematics, recursion theory or combinatory logic is presupposed, although this paper deals with quite general abstractions of standard results in those three areas. Our purpose is to show how some apparently diverse results in these areas can be derived from a common construction. In Section 1 we consider five classical fixed point arguments (or rather, generalizations …Read more
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220Gödel's incompleteness theoremsOxford University Press. 1992.Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinat…Read more
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78Uniform self-referenceStudia Logica 44 (4). 1985.Self-referential sentences have played a key role in Tarski's proof [9] of the non-definibility of arithmetic truth within arithmetic and Gödel's proof [2] of the incompleteness of Peano Arithmetic. In this article we consider some new methods of achieving self-reference in a uniform manner.
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6An epistemological nightmareIn Douglas R. Hofstadter & Daniel C. Dennett (eds.), The Mind's I, Basic Books. 1981.