Item description for Incompleteness in the Land of Sets (Studies in Logic) by Melvin Fitting...
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 Gdel, 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. Gdel 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 Gdel's Second Incompleteness Theorem. Exercises are scattered throughout.
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Est. Packaging Dimensions: Length: 9" Width: 5.9" Height: 0.5" Weight: 0.5 lbs.
Release Date Feb 19, 2007
Publisher College Publications
ISBN 1904987346 ISBN13 9781904987345
Availability 127 units. Availability accurate as of Jan 17, 2017 02:49.
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More About Melvin Fitting
Fitting, Lehman College and Graduate Center, City University of New York, USA.
Melvin Fitting was born in 1942 and has an academic affiliation as follows - City University of New York.