Faculty Book: Melvin Fitting
Incompleteness in the Land of Sets
(College Publications, 2007)
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. Melvin Fitting is a professor of computer science, mathematics, and philosophy at Lehman College and the Graduate Center.
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Submitted on: FEB 19, 2007