An Algebraic Introduction to Mathematical Logic

D.W. Barnes, J.M. Mack (Autoren)

Buch | Softcover

123 Seiten

2013 | Softcover reprint of the original 1st ed. 1975
Springer-Verlag New York Inc.
978-1-4757-4491-0 (ISBN)

Artikel merken

This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a substantial course on abstract algebra. Consequently, our treatment of the subject is algebraic. Although we assume a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of the exercises. We also assume a familiarity with the main ideas of set theory, including cardinal numbers and Zorn's Lemma. In this book, we carry out a mathematical study of the logic used in mathematics. We do this by constructing a mathematical model of logic and applying mathematics to analyse the properties of the model. We therefore regard all our existing knowledge of mathematics as being applicable to the analysis of the model, and in particular we accept set theory as part of the meta-Ianguage. We are not attempting to construct a foundation on which all mathematics is to be based--rather, any conclusions to be drawn about the foundations of mathematics come only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory.

I Universal Algebra.- II Propositional Calculus.- III Properties of the Propositional Calculus.- IV Predicate Calculus.- V First-Order Mathematics.- VI Zermelo-Fraenkel Set Theory.- VII Ultraproducts.- VIII Non-Standard Models.- IX Turing Machines and Gödel Numbers.- X Hilbert’s Tenth Problem, Word Problems.- References and Further Reading.- Index of Notations.

Reihe/Serie	Graduate Texts in Mathematics ; 22
Zusatzinfo	IX, 123 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	1-4757-4491-9 / 1475744919
ISBN-13	978-1-4757-4491-0 / 9781475744910
Zustand	Neuware