A course in mathematical logic for mathematicians:
Gespeichert in:
| Vorheriger Titel: | Manin, Jurij I. A course in mathematical logic |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2010
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Graduate texts in mathematics
53 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Kap. I-VIII aus dem Russ. übers. |
| Beschreibung: | XVII, 384 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9781441906144 9781441906151 9781461424796 |
Internformat
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| 245 | 1 | 0 | |a A course in mathematical logic for mathematicians |c Yu. I. Manin |
| 250 | |a 2. ed. |b with new chapters by Boris Zilber and Yuri I. Manin | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2010 | |
| 300 | |a XVII, 384 S. |b graph. Darst. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 53 | |
| 500 | |a Kap. I-VIII aus dem Russ. übers. | ||
| 650 | 4 | |a Logic, Symbolic and mathematical | |
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| 700 | 1 | |a Zilber, Boris |e Sonstige |0 (DE-588)14102545X |4 oth | |
| 780 | 0 | 0 | |i 1. Auflage |a Manin, Jurij I. |t A course in mathematical logic |
| 830 | 0 | |a Graduate texts in mathematics |v 53 |w (DE-604)BV000000067 |9 53 | |
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Datensatz im Suchindex
| _version_ | 1805093238088925184 |
|---|---|
| adam_text |
Contents
Preface to the Second Edition. vii
Preface to the First Edition. xi
I PROVABILITY
I Introduction to Formal Languages. 3
1 General Information. 3
2 First-Order Languages. 5
Digression: Names. . * 9
3 Beginners’ Course in Translation. 9
Digression: Syntax. 15
II Truth and Deducibility. 19
1 Unique Reading Lemma. 19
2 Interpretation: Truths Definability. 23
3 Syntactic Properties of Truth. 28
Digression: Natural Logic. 33
4 Deducibility. 36
Digression: Proof. 45
5 Tautologies and Boolean Algebras. 49
Digression: Kennings. 53
6 Godel’s Completeness Theorem . 55
7 Countable Models and Skolem’s Paradox. 61
8 Language Extensions. 66
9 Undefinability of Truth: The Language SELF. 69
10 Smullyan’s Language of Arithmetic. 71
11 Undefinability of T’uth: Tarski’s Theorem . 74
Digression: Self-Reference. 77
12 Quantum Logic. 78
Appendix: The Von Neumann Universe. 89
The Last Digi'ession. Tmth as Value and Duty: Lessons of
Mathematics. 96
III The Continuum Problem and Forcing. 105
1 The Problem: Results, Ideas . .105
2 A Language of Real Analysis. . 110
3 The Continuum Hypothesis Is Not Deducible in L2 Real. 114
XVI
Contents
4 Boolean-Valued Universes.120
5 The Axiom of Extensionality Is “True”.124
6 The Axioms of Pairing, Union, Power Set, and
Regularity Are “True” .127
7 The Axioms of Infinity, Replacement, and
Choice Are “True”.132
8 The Continuum Hypothesis Is “False” for Suitable B.140
9 Forcing.145
IV The Continuum Problem and Constructible Sets .151
1 Gôdel's Constructible Universe. 151
2 Definability and Absoluteness.155
3 The Constructible Universe as a Model for Set Theory.158
4 The Generalized Continuum Hypothesis Is L-True. 161
5 Constructibility Formula.164
6 Remarks on Formalization.171
7 What Is the Cardinality of the Continuum?.172
II COMPUTABILITY
V Recursive Functions and Church’s Thesis.179
1 Introduction. Intuitive Computability.179
2 Partial Recursive Functions.183
3 Basic Examples of Recursiveness.187
4 Enumerable and Decidable Sets.191
5 Elements of Recursive Geometry.201
VI Diophantine Sets and Algorithmic Undecidability.207
1 The Basic Result.207
2 Plan of Proof.209
3 Enumerable Sets Are ID-Sets. 211
4 The Reduction.214
5 Construction of a Special Diophantine Set.217
6 The Graph of the Exponential Is Diophantine.221
7 The Factorial and Binomial Coefficient Graphs
Are Diophantine.221
8 Versai Families.223
9 Kolmogorov Complexity.226
III PROVABILITY AND COMPUTABILITY
VII Godel’s Incompleteness Theorem .235
1 Arithmetic of Syntax .235
2 Incompleteness Principles.240
3 Nonenumerability of True Formulas.241
Contents xvii
4 Syntactic Analysis.243
5 Enumerability of Deducible Formulas.249
6 The Arithmetical Hierarchy.252
7 Productivity of Arithmetical Truth. 255
8 On the Length of Proofs.258
VIII Recursive Groups.263
1 Basic Result and Its Corollaries.263
2 Free Products and HNN-Extensions.266
3 Embeddings in Groups with Two Generators.270
4 Benign Subgroups.271
5 Bounded Systems of Generators.275
6 End of the Proof.280
IX Constructive Universe and Computation.285
1 Introduction: A Categorical View of Computation.285
2 Expanding Constructive Universe: Generalities .289
3 Expanding Constructive Universe: Morphisms.293
4 Operads and PROPs.296
5 The World of Graphs as a Topological Language .298
6 Models of Computation and Complexity.307
7 Basics of Quantum Computation I: Quantum Entanglement . . 315
8 Selected Quantum Subroutines.319
9 Shor’s Factoring Algorithm.322
10 Kolmogorov Complexity and Growth of Recursive Functions . 325
IV MODEL THEORY
X Model Theory.331
1 Languages and Structures.331
2 The Compactness Theorem. 334
3 Basic Methods and Constructions .342
4 Completeness and Quantifier Elimination in Some Theories . . . 350
5 Classification Theory .359
6 Geometric Stability Theory. 364
7 Other Languages and Nonelementary Model Theory.374
Suggestions for Further Reading.379
Index.381 |
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| dewey-full | 511.3 |
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| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| spelling | A course in mathematical logic for mathematicians Yu. I. Manin 2. ed. with new chapters by Boris Zilber and Yuri I. Manin New York [u.a.] Springer 2010 XVII, 384 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 53 Kap. I-VIII aus dem Russ. übers. Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Mathematische Logik (DE-588)4037951-6 s DE-604 Manin, Jurij I. 1937-2023 Sonstige (DE-588)121177580 oth Zilber, Boris Sonstige (DE-588)14102545X oth 1. Auflage Manin, Jurij I. A course in mathematical logic Graduate texts in mathematics 53 (DE-604)BV000000067 53 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3264873&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018703240&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | A course in mathematical logic for mathematicians Graduate texts in mathematics Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4151278-9 |
| title | A course in mathematical logic for mathematicians |
| title_auth | A course in mathematical logic for mathematicians |
| title_exact_search | A course in mathematical logic for mathematicians |
| title_full | A course in mathematical logic for mathematicians Yu. I. Manin |
| title_fullStr | A course in mathematical logic for mathematicians Yu. I. Manin |
| title_full_unstemmed | A course in mathematical logic for mathematicians Yu. I. Manin |
| title_old | Manin, Jurij I. A course in mathematical logic |
| title_short | A course in mathematical logic for mathematicians |
| title_sort | a course in mathematical logic for mathematicians |
| topic | Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Logic, Symbolic and mathematical Mathematische Logik Einführung |
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