# Mathematical Logic

Springer, Jun 10, 1994 - Mathematics - 308 pages
This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most striking results are contained in Goedel's work: First, it is possible to give a simple set of rules that suffice to carry out all mathematical proofs; but, second, these rules are necessarily incomplete - it is impossible, for example, to prove all true statements of arithmetic. The book begins with an introduction to first-order logic, Goedel's theorem, and model theory. A second part covers extensions of first-order logic and limitations of the formal methods. The book covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem. Fraissé's elementary equivalence, and Lindstroem's theorem on the maximality of first-order logic.

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#### Review: Mathematical Logic

User Review  - Joecolelife - Goodreads

The formal mathematics is organized and presented so clearly and precisely that I felt I was admiring a fine crystal structure. The notation used may seem excessive to some, but it actually is the ... Read full review

### References from web pages

Structure (mathematical logic) - Wikipedia, the free encyclopedia
Structure (mathematical logic) ..... A Course in Model Theory: An Introduction to Contemporary Mathematical Logic, Berlin, New York: Springer-Verlag, ...
en.wikipedia.org/ wiki/ Structure_(mathematical_logic)

Ebbinghaus, Flum, Thomas. Mathematical Logic.
Chapter 1: Introduction--provides motivational text (distinguishing between traditional philosophical logic and mathematical logic) and motivational ...
mathgate.info/ cebrown/ notes/ ebbinghaus.php

JSTOR: Mathematical Logic
It broadly follows the lines that are taken by the majority of mathematical logic text books as regards choice of topics, notation, definitions, ...

Ebbinghaus H.-D., Flum J., Thomas W. Mathematical logic (ISBN 0 ...
Ebbinghaus H.-D., Flum J., Thomas W. Mathematical logic (ISBN 0-387-90895-1)(Springer, 1984)(L)(T)(113s).djvu. Size 2.1Mb Date Sep 17, 2004 ...
www.eknigu.org/ info/ M_Mathematics/ MA_Algebra/ MAml_Mathematical%20logic/ Ebbinghaus%20H.-D.,%20Flum%20J.,%20Thomas%20W...

Basic Library List-Foundations and Mathematical Logic
Andrews, Peter B. An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof New York, NY: Academic Press, 1986. ...
www.maa.org/ BLL/ foundations.htm

CIDEC Library: Ebbinghaus * Mathematical Logic
MATHEMATICAL LOGIC 2nd ed. Uniform Title: Einführung in die mathematisch Logik. English Translated from the German by Ferebee, as ...
cs.ioc.ee/ yik/ lib/ 1/ Ebbinghaus2.html

MATHEMATICAL STRUCTURES RESEARCH
"Axioms for Abstract Model Theory",Annals of Mathematical Logic 7(1974) 221-265. ... Mathematical Logic. Springer-Verlag 1984. Ebbinghaus and Flum. ...
www.mmsysgrp.com/ mathstrc.htm

FINITE MODEL THEORY (Perspectives in Mathematical Logic) By Heinz ...
FINITE MODEL THEORY (Perspectives in Mathematical Logic) By Heinz-Dieter Ebbinghaus and Jorg Flum: 327 pp., DM. 148.–, ISBN 3 540 60149 X (Springer, 1995). ...
journals.cambridge.org/ abstract_S0024609396222416

Abstract Math: Mathematical Reasoning
Mathematical logic (or proof theory) is a branch of mathematics that uses mathematical ... Mathematical logic is quite technical but very powerful; ...
www.abstractmath.org/ MM/ MMMathReasoning.htm

18.511: Mathematical Logic
Description, This course provides an introduction to mathematical logic. ... Text, Mathematical Logic, by Ebbinghaus, Flum, and Thomas (Springer 1994) ...
www-math.mit.edu/ ~rosen/ 18.511/

### About the author (1994)

Prof. Jvrg Flum, Abteilung f]r Mathematische Logik, Albert-Ludwigs-Universitdt Freiburg, Germany, http: //logik.mathematik.uni-freiburg.de/personen/Flum.html Prof. Martin Grohe, Institut f]r Informatik, Humboldt-Universitdt zu Berlin, Germany, http: //www.informatik.hu-berlin.de/~grohe/ The authors are very well qualified to write this book. In addition to their strong backgrounds in complexity, algorithms, etc., they have contributed a number of specific key results in parameterized complexity (e.g., http: //epubs.siam.org/sam-bin/dbq/article/42720). Jvrg Flum has coauthored two other Springer monographs: (i) "Mathematical Logic," Undergraduate Texts in Mathematics, 0-387-94258-0, 3rd printing since 1994, over 4000 copies sold, Heinz-Dieter Ebbinghaus, Jvrg Flum, Wolfgang Thomas, http: //www.springer.com/0-387-94258-0. (ii) "Finite Model Theory," Springer Monographs in Mathematics (was in series Perspectives in Mathematical Logic), printed in soft- and hardback, 1995, 2nd ed. in 1999, 2nd corr. print in 2006, Heinz-Dieter Ebbinghaus, Jvrg Flum, 3-540-28787-6, http: //www.springer.com/3-540-28787-6. In addition, Jvrg Flum coauthored the following LNM title: Vol. 769, "Topological Model Theory, 1980, 3-540-09732-5, Jvrg Flum, Martin Ziegler. And he coedited the following LNCS title: Vol. 1683, CSL 1999 conf. proc., Jvrg Flum, Mario Rodriguez-Artalejo, 1999, 3-540-66536-6. Prof. Martin Grohe has authored over 50 articles for refereed theoretical computer science journals and conference proceedings (http: //www.informatik.uni-trier.de/~ley/db/indices/a-tree/g/Grohe: Martin.html) in the areas of logic, complexity, algorithms, etc.

Prof. Dr. Heinz-Dieter Ebbinghaus und Prof. Dr. JArg Flum forschen und lehren am Institut fA1/4r Mathematik der UniversitAt Freiburg, Prof. Dr. Wolfgang Thomas ist Inhaber des Lehrstuhls fA1/4r Informatik 7 (Logik und Theorie diskreter Systeme) der RWTH Aachen.