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Mathematical Logic
Heinz-Dieter Ebbinghaus, Jörg Flum, Wolfgang Thomas (Gebundene Ausgabe, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
29.05.2021
Sprache
Englisch
EAN
9783030738389
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Graduate Texts in Mathematics
Sonderedition
Nein
Autor
Heinz-Dieter Ebbinghaus, Jörg Flum, Wolfgang Thomas
Seitenanzahl
304
Auflage
3
Einbandart
Gebundene Ausgabe
Schlagwörter
First-order logic, First-order language, Gödel’s completeness theorem, Mathematical provability, Model theory logic, Axiom system logic, Trakhtenbrot’s theorem, Computability logic, Herbrand's theorem, Logic computer science, Propositional logic, Second-order logic, Infinitary languages, Lindström’s theorem, Presburger arithmetic, Weak monadic second order, Mathematical logic textbook, Graduate mathematical logic textbook
Thema-Inhalt
PBCD - Mathematik: Logik
PBC - Mathematische Grundlagen
UYAM - Mathematik für Informatiker
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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