Introduction to Mathematical Logic (The Wadsworth & Brooks/Cole Mathematics Series)

Elliot Mendelsohn

ISBN 10: 1461572908 / ISBN 13: 9781461572909

Published by Springer, 2012

About this Item

reprint edition. 352 pages. 9.61x6.69x0.90 inches. In Stock.

Seller Inventory # x-1461572908

Bibliographic Details

• Title: Introduction to Mathematical Logic (The Wadsworth & Brooks/Cole Mathematics Series)
• Publisher: Springer
• Publication Date: 2012
• Language: English
• ISBN 10: 1461572908
• ISBN 13: 9781461572909
• Binding: Paperback
• Condition: Brand New
• Weight: 0.5 kilograms

About this title

Synopsis

This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.