Incompleteness in the Land of Sets
Language: English
Published by College Publications, 2007
- Softcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
AbeBooks seller since August 14, 2006
Condition: New
£ 35.42
Quantity: 2 available
Add to basketItem description from seller
nach der Bestellung gedruckt Neuware - Printed after ordering - Russell'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 Gödel, 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. Gödel 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 Gödel's Second Incompleteness Theorem. Exercises are scattered throughout.…
Seller Inventory # 9781904987345
- Title
- Incompleteness in the Land of Sets
- Author
- M. Fitting
- Publisher
- College Publications
- Publication year
- 2007
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 1904987346
- ISBN 13
- 9781904987345
- Item weight
- 248 grams
- Dimensions
- 234x156x9 mm
"Synopsis" may belong to another edition of this title.
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