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Incompleteness in the Land of Sets (Studies in Logic) [Paperback]

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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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Item Specifications...

Pages   156
Est. Packaging Dimensions:   Length: 9" Width: 5.9" Height: 0.5"
Weight:   0.5 lbs.
Binding  Softcover
Release Date   Feb 19, 2007
Publisher   College Publications
ISBN  1904987346  
ISBN13  9781904987345  

Availability  127 units.
Availability accurate as of Oct 24, 2016 09:37.
Usually ships within one to two business days from La Vergne, TN.
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More About Melvin Fitting

Register your artisan biography and upload your photo! 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.

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Product Categories

1Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Logic
2Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Set Theory
3Books > Subjects > Science > General
4Books > Subjects > Science > Mathematics > General
5Books > Subjects > Science > Mathematics > Pure Mathematics > Logic
6Books > Subjects > Science > Mathematics > Pure Mathematics > Set Theory

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