Adamowicz / Zbierski Logic of Mathematics

A Modern Course of Classical Logic
1. Auflage 2011
ISBN: 978-1-118-03079-0
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 272 Seiten, E-Book

Reihe: Wiley Series in Pure and Applied Mathematics

A thorough, accessible, and rigorous presentation of the centraltheorems of mathematical logic . . . ideal for advanced students ofmathematics, computer science, and logic
Logic of Mathematics combines a full-scale introductory course inmathematical logic and model theory with a range of speciallyselected, more advanced theorems. Using a strict mathematicalapproach, this is the only book available that contains completeand precise proofs of all of these important theorems:
* Gödel's theorems of completeness and incompleteness
* The independence of Goodstein's theorem from Peanoarithmetic
* Tarski's theorem on real closed fields
* Matiyasevich's theorem on diophantine formulas
Logic of Mathematics also features:
* Full coverage of model theoretical topics such as definability,compactness, ultraproducts, realization, and omission oftypes
* Clear, concise explanations of all key concepts, from Booleanalgebras to Skolem-Löwenheim constructions and othertopics
* Carefully chosen exercises for each chapter, plus helpfulsolution hints
At last, here is a refreshingly clear, concise, and mathematicallyrigorous presentation of the basic concepts of mathematicallogic-requiring only a standard familiarity with abstract algebra.Employing a strict mathematical approach that emphasizes relationalstructures over logical language, this carefully organized text isdivided into two parts, which explain the essentials of the subjectin specific and straightforward terms.
Part I contains a thorough introduction to mathematical logic andmodel theory-including a full discussion of terms, formulas, andother fundamentals, plus detailed coverage of relational structuresand Boolean algebras, Gödel's completeness theorem, models ofPeano arithmetic, and much more.
Part II focuses on a number of advanced theorems that are centralto the field, such as Gödel's first and second theorems ofincompleteness, the independence proof of Goodstein's theorem fromPeano arithmetic, Tarski's theorem on real closed fields, andothers. No other text contains complete and precise proofs of allof these theorems.
With a solid and comprehensive program of exercises and selectedsolution hints, Logic of Mathematics is ideal for classroom use-theperfect textbook for advanced students of mathematics, computerscience, and logic.

Autoren/Hrsg.

Adamowicz, Zofia

Zbierski, Pawel

Inhaltsverzeichnis

Partial table of contents:
MATHEMATICAL STRUCTURES AND THEIR THEORIES.
Relational Systems.
Boolean Algebras.
Terms and Formulas.
Substitution of Terms.
Theorems and Proofs.
Generalization Rule and Elimination of Constants.
Peano Arithmetic.
Ultraproducts.
Supplementary Questions.
SELECTED TOPICS.
Total Functions.
Incompleteness of Arithmetic.
Tarski's Theorem.
Matiyasevich's Theorem.
Guide to Further Reading.
References.
Index.

Über Autor(innen)

ZOFIA ADAMOWICZ, PhD, is a professor at the Institute ofMathematics of the Polish Academy of Sciences in Warsaw.
PAWEL ZBIERSKI, PhD, is a professor at the Department ofMathematics at Warsaw University and the coauthor of Hausdorff Gapsand Limits.