  View Basket     AiML Academia Brasileira de Filosofia Algorithmics Cadernos de Lógica e Computação Cadernos de Lógica e Filosofia Cahiers de Logique et d'Epistemologie Communication, Mind and Language Computing Cuadernos de lógica, Epistemología y Lenguaje DEON Dialogues Economics Encyclopaedia of Logic Filosofia Handbooks Historia Logicae IfColog series in Computational Logic Journal of Applied Logics - IfCoLog Journal Journals Landscapes Logics for New-Generation AI Logic and Law Logic and Semiotics Logic PhDs Logic, Methodology and Philosophy of Science The Logica Yearbook Neural Computing and Artificial Intelligence Philosophy Research The SILFS series Studies in Logic History of Logic Logic and cognitive systems Mathematical logic and foundations Studies in Logic and Argumentation Studies in Talmudic Logic Systems Texts in Logic and Reasoning Texts in Mathematics Tributes Other Digital Downloads Information for authors About us Search for Books  Studies in Logic Back Incompleteness in the Land of SetsMelvin Fitting RussellÆs paradox arises when we consider those sets that do not belong to themselves. The collection of such sets cannot constitute a set. Step back a bit. Logical formulas define sets (in a standard model). Formulas, being mathematical objects, can be thought of as sets themselvesŚmathematics reduces to set theory. Consider those formulas that do not belong to the set they define. The collection of such formulas is not definable by a formula, by the same argument that Russell used. This quickly gives TarskiÆs result on the undefinability of truth. Variations on the same idea yield the famous results of G÷del, Church, Rosser, and Post.This book gives a full presentation of the basic incompleteness and undecidability theorems of mathematical logic in the framework of set theory. Corresponding results for arithmetic follow easily, and are also given. G÷del numbering is generally avoided, except when an explicit connection is made between set theory and arithmetic. The book assumes little technical background from the reader. One needs mathematical ability, a general familiarity with formal logic, and an understanding of the completeness theorem, though not its proof. All else is developed and formally proved, from TarskiÆs Theorem to G÷delÆs Second Incompleteness Theorem. Exercises are scattered throughout.February 2007ISBN 9781904987345Buy from Amazon: UK   US   Review

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