This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

Mathematical Logic, 2nd Edition (Undergraduate Texts in Mathematics)

Science & Math

Thomas, Wolfgang

Flum, J.

Ebbinghaus, H.D.

Mathematics

Springer

Mathematical Logic (Graduate Texts in Mathematics)

Product Description 
This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming. 
 From the Back Cover 
This textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions. What is a mathematical proof? How can mathematical proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs? In answering these questions, this textbook explores the capabilities and limitations of algorithms and proof methods in mathematics and computer science. 
The chapters are carefully organized, featuring complete proofs and numerous examples throughout. Beginning with motivating examples, the book goes on to present the syntax and semantics of first-order logic. After providing a sequent calculus for this logic, a Henkin-type proof of the completeness theorem is given. These introductory chapters prepare the reader for the advanced topics that follow, such as Gödel's Incompleteness Theorems, Trakhtenbrot's undecidability theorem, Lindström's theorems on the maximality of first-order logic, and results linking logic with automata theory. This new edition features many modernizations, as well as two additional important results: The decidability of Presburger arithmetic, and the decidability of the weak monadic theory of the successor function. 
Mathematical Logic is ideal for students beginning their studies in logic and the foundations of mathematics. Although the primary audience for this textbook will be graduate students or advanced undergraduates in mathematics or computer science, in fact the book has few formal prerequisites. It demands of the reader only mathematical maturity and experience with basic abstract structures, such as those encountered in discrete mathematics or algebra. 
 About the Author 
Heinz-Dieter Ebbinghaus is Professor Emeritus at the Mathematical Institute of the University of Freiburg. His work spans fields in logic, such as model theory and set theory, and includes historical aspects. 
Jörg Flum is Professor Emeritus at the Mathematical Institute of the University of Freiburg. His research interests include mathematical logic, finite model theory, and parameterized complexity theory. 
Wolfgang Thomas is Professor Emeritus at the Computer Science Department of RWTH Aachen University. His research interests focus on logic in computer science, in particular logical aspects of automata theory.

Mathematical Logic (Graduate Texts in Mathematics, 291)

Computers & Technology

Ebbinghaus, Heinz-Dieter

Flum, Jörg

Computer Science

This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

Lehrbuch der Chemie für die Sekundarstufe II, Chemisches Gleichgewicht, Thermodynamik, Reaktionskinetik

Liening, Bernard

Quante, Uwe

Diesterweg

Was ist ein mathematischer Beweis? Wie lassen sich Beweise rechtfertigen? Gibt es Grenzen der Beweisbarkeit? Ist die Mathematik widerspruchsfrei? Kann man das Auffinden mathematischer Beweise Computern übertragen? Erst im 20. Jahrhundert ist es der mathematischen Logik gelungen, weitreichende Antworten auf diese Fragen zu geben. Im vorliegenden Werk werden die Ergebnisse systematisch zusammengestellt; im Mittelpunkt steht dabei die Logik erster Stufe. 
Die Lektüre setzt – außer einer gewissen Vertrautheit mit der mathematischen Denkweise – keine spezifischen Kenntnisse voraus. 
Für die vorliegende 6. Auflage wurde der Text überarbeitet und durch die Darstellung zweier für Logik und Informatik wichtiger Entscheidbarkeitsresultate erweitert.

Einführung in die mathematische Logik (German Edition)

Springer Spektrum

See the best price to sell, buy, or rent books by Thomas, Wolfgang. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Thomas, Wolfgang