Mathematical Logic

by Stephen Cole Kleene

Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text. It begins with an elementary but thorough overview of mathematical logic of first order. The treatment extends beyond a single method of formulating logic to offer instruction in a variety of model theory (truth tables), Hilbert-type proof theory, and proof theory handled through derived rules.The second part supplements the previously discussed material and introduces some of the newer ideas and the more profound results of twentieth-century logical research. Subsequent chapters explore the study of formal number theory, with surveys of the famous incompleteness and undecidability results of Godel, Church, Turing, and others. The emphasis in the final chapter reverts to logic, with examinations of Godel's completeness theorem, Gentzen's theorem, Skolem's paradox and nonstandard models of arithmetic, and other theorems. The author, Stephen Cole Kleene, was Cyrus C. MacDuffee Professor of Mathematics at the University of Wisconsin, Madison. Preface. Bibliography. Theorem and Lemma Pages. List of Postulates. Symbols and Notations. Index.

Genres: Mathematics, Logic, Philosophy, Nonfiction, Computer Science, Reference

514 pages, Kindle Edition

First published January 1, 1967

Reviews

[Ragdoll Metaphysics · Rating 5 out of 5]

Good starter text - am using it to prepare for a class and the exercises. You are expected to try to memorize or at least familiarize yourself with some theorems and lemmas but these are generally intuitive once you have gotten use to the symbolism. The problem sets help as well.

[Guy M · Rating 4 out of 5]

Still a good intro to model theory, proof theory, basic first-order logic, and some neat historical notes on the foundations of mathematics (Godel's proofs, the "war" between the formalists and intuitionists, etc.)

[Ryan O'neil · Rating 5 out of 5]

Great book, but one piece of advice before you read; find a PDF or intro-to-course online that introduces some of the basic concepts because the author jumps right in pretty quickly.