04073nam 22006135 450 991048073210332120210915185544.01-4757-2355-510.1007/978-1-4757-2355-7(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 H.-Dauthttp://id.loc.gov/vocabulary/relators/aut1045262Flum Jauthttp://id.loc.gov/vocabulary/relators/autThomas Wolfgangauthttp://id.loc.gov/vocabulary/relators/autBOOK9910480732103321Mathematical Logic2471401UNINA01595oam 2200421zu 450 99621780160331620210807003341.0(CKB)111026746746436(SSID)ssj0000445479(PQKBManifestationID)12129128(PQKBTitleCode)TC0000445479(PQKBWorkID)10485621(PQKB)10518853(EXLCZ)9911102674674643620160829d1997 uy engtxtccrPacific Rim International Symposium on Fault-Tolerant Systems : proceedings : December 15-16, 1997, National Taiwan University, Taipei, Taiwan[Place of publication not identified]IEEE Computer Society Press1997Bibliographic Level Mode of Issuance: Monograph0-8186-8212-4 Fault-tolerant computingCongressesEngineering & Applied SciencesHILCCComputer ScienceHILCCFault-tolerant computingCongressesEngineering & Applied SciencesComputer Science004IEEE Computer Society Fault-Tolerant Computing Technical Committee.Kuo li T?ai-wan ta hsüehPacific Rim International Symposium on Fault Tolerant SystemsPQKBBOOK996217801603316Pacific Rim International Symposium on Fault-Tolerant Systems : proceedings : December 15-16, 1997, National Taiwan University, Taipei, Taiwan2380664UNISA00983nam a22002651i 450099100379933970753620030921153445.0031111s1992 uika||||||||||||||||eng 0582067596b1247552x-39ule_instARCHE-050880ExLDip.to LingueitaA.t.i. Arché s.c.r.l. Pandora Sicilia s.r.l.428Naylor, Helen254532Paths to proficiency /Helen Naylor, Stuart HaggerHarlow :Longman,1992v. :ill. ;26 cmLingua ingleseManualiHagger, Stuartauthorhttp://id.loc.gov/vocabulary/relators/aut254533.b1247552x02-04-1413-11-03991003799339707536LE012 D 431V. 112012000073432le012-E0.00-l- 00000.i1290727313-11-03Paths to proficiency1459523UNISALENTOle01213-11-03ma -enguik01