Mathematical logic

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"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."--Publisher's description

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Title Statements

Full title :Mathematical logic / Heinz-Dieter Ebbinghaus, Jörg Flum, Wolfgang Thomas.

Summary

Edition Statements

Publication Date:2021
Edition:Third edition

Publication Statements

Publisher(s):Springer
Place of Publication:Cham, Switzerland
Language:eng
Publication Date:2021

The Physical Object

Description:ix, 304 pages : : illustrations ; : 25 cm

Edition Identifiers

ISBN:9783030738389, 3030738388
oclc:on1243743218
LC Classification:QA9
Dewey Decimal:511.3

A -- I Introduction -- II Syntax of First-Order Languages -- III Semantics of First-Order Languages -- IV A Sequent Calculus -- V The Completeness Theorem -- VI The Löwenheim-Skolem and the Compactness Theorem -- VII The Scope of First-Order Logic -- VIII Syntactic Interpretations and Normal Forms -- B -- IX Extensions of First-Order Logic -- X Computability and Its Limitations -- XI Free Models and Logic Programming -- XII An Algebraic Characterization of Elementary Equivalence -- XIII Lindström's Theorems -- References -- List of Symbols -- Subject Index.