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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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34Set 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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16Mind 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.
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11An 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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59Recursion 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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32Monadic Elementary Formal SystemsZeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (6): 81-83. 1961.
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36The 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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100Some 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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223Gödel'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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84Uniform 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.
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7Puzzles of logic involve knights, knaves, gods, demons, and mortals, and Inspector Craig conducts a summer-long adventure in combinatory logic, basic to computer science and artificial intelligence
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24Review: Willard Van Orman Quine, Methods of Logic (review)Journal of Symbolic Logic 24 (3): 219-220. 1959.
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117First-order logicSpringer Verlag. 1968.This completely self-contained study, widely considered the best book in the field, is intended to serve both as an introduction to quantification theory and as ...