Mathematical Logic [[electronic resource] /] / by H.-D. Ebbinghaus, J. Flum, Wolfgang Thomas

• Autore: Ebbinghaus H.-D
• Pubblicazione: New York, NY : , : Springer New York : , : Imprint : Springer, , 1994
• Edizione: 2nd ed. 1994.
• Descrizione fisica: 1 online resource (X, 291 p.)
• Disciplina: 511.3
• Soggetto topico: Mathematical logic; Mathematics—Study and teaching ; Mathematical Logic and Foundations; Mathematics Education
• Classificazione: 03-01
• Persona (resp. second.): FlumJ; ThomasWolfgang
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and indexes.
• Nota di contenuto: 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 Limitations of the Formal Method -- XI Free Models and Logic Programming -- XII An Algebraic Characterization of Elementary Equivalence -- XIII Lindström’s Theorems -- References -- Symbol Index.
• Sommario/riassunto: What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathe­ matical proofs? Only in this century has there been success in obtaining substantial and satisfactory answers. The present book contains a systematic discussion of these results. The investigations are centered around first-order logic. Our first goal is Godel's completeness theorem, which shows that the con­ sequence relation coincides with formal provability: By means of a calcu­ lus consisting of simple formal inference rules, one can obtain all conse­ quences of a given axiom system (and in particular, imitate all mathemat­ ical proofs). A short digression into model theory will help us to analyze the expres­ sive power of the first-order language, and it will turn out that there are certain deficiencies. For example, the first-order language does not allow the formulation of an adequate axiom system for arithmetic or analysis. On the other hand, this difficulty can be overcome--even in the framework of first-order logic-by developing mathematics in set-theoretic terms. We explain the prerequisites from set theory necessary for this purpose and then treat the subtle relation between logic and set theory in a thorough manner.
• Titolo autorizzato: Mathematical Logic
• ISBN: 1-4757-2355-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910480732103321
• Lo trovi qui: Univ. Federico II
• Serie: Undergraduate Texts in Mathematics, . 0172-6056