A course in mathematical logic:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
North-Holland Publ.
1977
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 599 S. graph. Darst. |
| ISBN: | 0720428440 |
Staff View
MARC
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| 245 | 1 | 0 | |a A course in mathematical logic |c by J. L. Bell and M. Machover |
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Record in the Search Index
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CONTENTS Acknowledgements. IX Interdependence scheme for the chapters. XIV Introduction. XV Recommended reading. XIX Chapter 0. Prerequisites. 1 CHAPTER 1. Beginning mathematical logic. 5 §1 . General considerations . 5 §2 . Structures and formal languages. 9 §3 . Higher-order languages. 14 §4 . Basic syntax. 15 §5 . Notational conventions. 18 §6 . Propositional semantics. 20 §7 . Propositional tableaux. 25 §8 . The Elimination Theorem for propositionaltableaux. 31 §9 . Completeness of propositional
tableaux. 33 §10 . The propositional calculus. 34 §11 . The propositional calculus and tableaux. 40 §12 . Weak completeness of the propositionalcalculus. 43 §13 . Strong completeness of the propositionalcalculus. 44 §14 . Propositional logic based on ~1 and Λ . 46 §15 . Propositional logic based on “,— , A andV. 47 §16 . Historical and bibliographical remarks . 48 ■Chapter 2. First-order logic. 49 §1 . First-order semantics. 49 §2 . Freedom and bondage. 54 §3 . Substitution. 57 §4 . First-order tableaux.67 §5 . Some “book-keeping” lemmas. 72 §6 . The Elimination Theorem for first-order tableaux. 79 §7 . Hintikka
sets. 83 §8 . Completeness of first-order tableaux. 88 §9 . Prenex and Skolem forms . . 93 ■,§10. Elimination of function symbols. 97
CONTENTS XI §11 . Elimination of equality.101 §12 . Relativization. 102 §13 . Virtual terms.104 §14 . Historical and bibliographical remarks. 107 Chapter 3. First-order logic (Continued). 108 §1 . The first-order predicate calculus. 108 §2 . The first-order predicate calculus and tableaux. 115 §3 . Completeness of the first-order predicate calculus. 117 §4 . First-order logic based on 3. 122 §5 . What have we achieved?. 122 §6 . Historical and bibliographical remarks. 124 Chapter 4. Boolean Algebras. 125 §1 §2 §3 §4 §5 §6 §7 §8 . . . . . . . . Lattices . 125 Boolean
algebras. 129 Filters and homomorphisms. 133 The Stone Representation Theorem. 141 Atoms. 150 Duality for homomorphisms and continuous mappings. 153 The Rasiowa-Sikorski Theorem. 157 Historical and bibliographical remarks.159 Chapter 5. Model theory. 161 §1 . Basic ideas of model theory. 161 §2 . The Löwenheim-Skolem Theorems.168 §3 . Ultraproducts. 174 §4 . Completeness and categoricity. 184 §5 . Lindenbaum algebras. 191 §6 . Element types and Ro-categoricity. 203 §7 . Indiscernibles and models with
automorphisms. 214 §8 . Historical and bibliographical remarks. 224 Chapter 6. Recursion theory. 226 §1 . Basic notation and terminology. 226 §2 . Algorithmic functions and functionals. 230 §3 . The computer URIM.232 §4 . Computable functionals and functions. 237 §5 . Recursive functionals and functions. 239 §6 . A stockpile of examples. 247 §7 . Church’s Thesis. 257 §8 . Recursiveness of computable functionals.259 §9 . Functionals with several sequence arguments. 265 §10 . Fundamental theorems. 266 §11 . Recursively enumerable sets.277 §12 . Diophantine
relations. 284 §13 . The Fibonacci sequence. 288 §14 . The power function.296
χπ CONTENTS §15 §16 §17 . Bounded universal quantification. 305 . The MRDP Theorem and Hilbert’sTenth Problem. 311 . Historical and bibliographical remarks. 314 Chapter 7. Logic — Limitative results. 316 §1 . General notation and terminology.316 §2 . Nonstandard models of Ω. 318 §3 . Arithmeticity . 324 §4 . Tarski’s Theorem. 327 §5 . Axiomatic theories. 332 §6 . Baby arithmetic. 334 §7 . Junior arithmetic. 336 §8 . A finitely axiomatized theory. 340 §9 . First-order Peano arithmetic.342 §10 .
Undecidability. 347 §11 . Incompleteness. 353 §12 . Historical and bibliographical remarks. 359 Chapter 8. Recursion theory (Continued). 361 §1 . The arithmetical hierarchy.361 §2 . A result concerning 7^. 369 §3 . Encoded theories. 370 §4 . Inseparable pairs of sets. 372 §5 . Productive and creative sets; reducibility. 376 §6 . One-one reducibility; recursive isomorphism. 384 §7 . Turing degrees. 388 §8 . Post’s problem and its solution. 392 §9 . Historical and bibliographical remarks. 398 Chapter 9. §1 §2 §3 §4 §5 §6 §7 §8 §9 §10 §11 §12 §13 §14 INTUITIONISTIC first-order
logic. 400 . Preliminary discussion. 400 . Philosophical remark. 403 . Constructive meaning of sentences. 403 . Constructive interpretations. 404 . Intuitionistic tableaux. 408 . Kripke’s semantics. 416 . The Elimination Theorem for intuitionistic tableaux. 422 . Intuitionistic propositional calculus.433 . Intuitionistic predicate calculus. 434 . Completeness . 438 . Translations from classical to intuitionistic logic.442 . The Interpolation Theorem. 445 . Some results in classical logic. 452 . Historical and bibliographical
remarks.457 Chapter 10. Axiomatic set theory.459 §1 . Basic developments.459 §2 . Ordinals . 468
CONTENTS XIII The Axiom of Regularity. 477 Cardinality and the Axiom of Choice. 487 Reflection Principles . . 491 The formalization of satisfaction. 497 Absoluteness. 502 Constructible sets.509 The consistency of AC and GCH. 516 Problems. 522 Historical and bibliographical remarks. 529 Chapter 11. Nonstandard analysis.531 §1 . Enlargements. 532 §2 . Zermelo structures and theirenlargements. 536 §3 . Filters and monads.543 §4 . Topology. 553
§5 . Topological groups. 561 §6 . The real numbers. 566 §7 . A methodological discussion. 572 §8 . Historical and bibliographicalremarks.573 §3 . §4 . §5 . §6 . §7 . §8 . §9 . §10 . §11 . Bibliography. 576 General index. 584 Index of symbols. 595 |
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| illustrated | Illustrated |
| indexdate | 2024-07-20T04:10:07Z |
| institution | BVB |
| isbn | 0720428440 |
| language | English |
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| physical | XVIII, 599 S. graph. Darst. |
| publishDate | 1977 |
| publishDateSearch | 1977 |
| publishDateSort | 1977 |
| publisher | North-Holland Publ. |
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| spelling | Bell, John Lane Verfasser aut A course in mathematical logic by J. L. Bell and M. Machover Amsterdam [u.a.] North-Holland Publ. 1977 XVIII, 599 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Modelltheorie (DE-588)4114617-7 gnd rswk-swf Ultraprodukt (DE-588)4127046-0 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s 1\p DE-604 Ultraprodukt (DE-588)4127046-0 s DE-604 Modelltheorie (DE-588)4114617-7 s Machover, Moshé Sonstige oth Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=011251001&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bell, John Lane A course in mathematical logic Mathematische Logik (DE-588)4037951-6 gnd Modelltheorie (DE-588)4114617-7 gnd Ultraprodukt (DE-588)4127046-0 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4114617-7 (DE-588)4127046-0 |
| title | A course in mathematical logic |
| title_auth | A course in mathematical logic |
| title_exact_search | A course in mathematical logic |
| title_full | A course in mathematical logic by J. L. Bell and M. Machover |
| title_fullStr | A course in mathematical logic by J. L. Bell and M. Machover |
| title_full_unstemmed | A course in mathematical logic by J. L. Bell and M. Machover |
| title_short | A course in mathematical logic |
| title_sort | a course in mathematical logic |
| topic | Mathematische Logik (DE-588)4037951-6 gnd Modelltheorie (DE-588)4114617-7 gnd Ultraprodukt (DE-588)4127046-0 gnd |
| topic_facet | Mathematische Logik Modelltheorie Ultraprodukt |
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