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[null,"1.","Record Nr.",null,"UNINA9910956106103321"]
[null,null,"Autore",null,"Ebbinghaus Heinz-Dieter <1939->"]
[null,null,"Titolo",null,"Mathematical Logic / / by H.-D. Ebbinghaus, J. Flum, Wolfgang Thomas"]
[null,null,"Pubbl/distr/stampa",null,"New York, NY : , : Springer New York : , : Imprint : Springer, , 1994"]
[null,null,"ISBN",null,"1-4757-2355-5"]
[null,null,"Edizione",null,"[2nd ed. 1994.]"]
[null,null,"Descrizione fisica",null,"1 online resource (X, 291 p.)"]
[null,null,"Collana",null,"Undergraduate Texts in Mathematics, , 2197-5604"]
[null,null,"Classificazione",null,"03-01"]
[null,null,"Disciplina",null,"511.3"]
[null,null,"Soggetti",null,"Logic, Symbolic and mathematical"]
[{"$nulls":4},"Mathematics - Study and teaching"]
[{"$nulls":4},"Mathematical Logic and Foundations"]
[{"$nulls":4},"Mathematics Education"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Bibliographic Level Mode of Issuance: Monograph"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and indexes."]
[null,null,"Nota di contenuto",null,"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."]
[null,null,null,"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 "]
[{"$nulls":4},"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."]