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Incompleteness in the Land of Sets by M. Fitting (2007, Perfect)

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About this product

Product Identifiers

PublisherCollege Publications

ISBN-101904987346

ISBN-139781904987345

eBay Product ID (ePID)60741662

Product Key Features

Number of Pages156 Pages

LanguageEnglish

Publication NameIncompleteness in the Land of Sets

Publication Year2007

SubjectSet Theory, Logic

TypeTextbook

AuthorM. Fitting

Subject AreaMathematics

FormatPerfect

Dimensions

Item Height0.3 in

Item Weight8.2 Oz

Item Length9.2 in

Item Width6.1 in

Additional Product Features

Dewey Edition22

Dewey Decimal511.322

SynopsisRussell's 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 themselves-mathematics 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 Tarski's 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 Tarski's Theorem to G del's Second Incompleteness Theorem. Exercises are scattered throughout.