04088nam 22006135 450 991079248760332120230825134723.01-4757-2355-510.1007/978-1-4757-2355-7(CKB)2660000000024224(SSID)ssj0001297533(PQKBManifestationID)11725945(PQKBTitleCode)TC0001297533(PQKBWorkID)11229082(PQKB)11271152(DE-He213)978-1-4757-2355-7(MiAaPQ)EBC3084680(PPN)238077004(EXLCZ)99266000000002422420130109d1994 u| 0engurnn#008mamaatxtccrMathematical Logic[electronic resource] /by H.-D. Ebbinghaus, J. Flum, Wolfgang Thomas2nd ed. 1994.New York, NY :Springer New York :Imprint: Springer,1994.1 online resource (X, 291 p.)Undergraduate Texts in Mathematics,0172-6056Bibliographic Level Mode of Issuance: Monograph0-387-94258-0 1-4757-2357-1 Includes bibliographical references and indexes.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.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.Undergraduate Texts in Mathematics,0172-6056Mathematical logicMathematics—Study and teaching Mathematical Logic and Foundationshttps://scigraph.springernature.com/ontologies/product-market-codes/M24005Mathematics Educationhttps://scigraph.springernature.com/ontologies/product-market-codes/O25000Mathematical logic.Mathematics—Study and teaching .Mathematical Logic and Foundations.Mathematics Education.511.303-01mscEbbinghaus Heinz-Dieter1939-authttp://id.loc.gov/vocabulary/relators/aut1068399Flum Jauthttp://id.loc.gov/vocabulary/relators/autThomas Wolfgangauthttp://id.loc.gov/vocabulary/relators/autBOOK9910792487603321Mathematical logic2553144UNINA01164nam0 22002891i 450 UON0033864320231205104249.68935-18-00259-720091015d1973 |0itac50 bagerDE|||| 1||||Mann ist Manndie Verwandlung des Packers galy Gay in den Militärbaracken von Kilkoa im Jahre neunzehnhundertfünfundzwanzigLustspielBertolt Brecht4. AuflFrankfurt am MainSuhrkamp197399 p.18 cm.001UON001728982001 Edition Suhrkamp210 Frankfurt am MainSuhrkamp259DEFrankfurt am MainUONL003175832Letteratura drammatica tedesca21BRECHTBertoltUONV11426836137SuhrkampUONV260759650ITSOL20240220RICASIBA - SISTEMA BIBLIOTECARIO DI ATENEOUONSIUON00338643SIBA - SISTEMA BIBLIOTECARIO DI ATENEOSI TED 25 I BRE 49 SI LO 3403 5 49 Mann ist Mann18645UNIOR