A course in mathematical logic for mathematicians:
Saved in:
| Previous Title: | Manin, Jurij I. A course in mathematical logic |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2010
|
| Edition: | 2. ed. |
| Series: | Graduate texts in mathematics
53 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Kap. I-VIII aus dem Russ. übers. |
| Physical Description: | XVII, 384 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9781441906144 9781441906151 9781461424796 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV035845025 | ||
| 003 | DE-604 | ||
| 005 | 20180814 | ||
| 007 | t | ||
| 008 | 091125s2010 d||| |||| 00||| eng d | ||
| 015 | |a 09,N15,0642 |2 dnb | ||
| 016 | 7 | |a 99339664X |2 DE-101 | |
| 020 | |a 9781441906144 |c Print |9 978-1-4419-0614-4 | ||
| 020 | |a 9781441906151 |c ebook |9 978-1-4419-0615-1 | ||
| 020 | |a 9781461424796 |9 978-1-4614-2479-6 | ||
| 024 | 3 | |a 9781441906144 | |
| 028 | 5 | 2 | |a 12617210 |
| 035 | |a (OCoLC)436030792 | ||
| 035 | |a (DE-599)DNB99339664X | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-20 |a DE-706 |a DE-384 |a DE-11 |a DE-188 |a DE-83 |a DE-521 |a DE-739 |a DE-355 | ||
| 050 | 0 | |a QA9 | |
| 082 | 0 | |a 511.3 |2 22 | |
| 084 | |a SK 130 |0 (DE-625)143216: |2 rvk | ||
| 084 | |a 03-01 |2 msc | ||
| 084 | |a 510 |2 sdnb | ||
| 084 | |a 03-XX |2 msc | ||
| 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 | |
| 650 | 0 | 7 | |a Mathematische Logik |0 (DE-588)4037951-6 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 689 | 0 | 0 | |a Mathematische Logik |0 (DE-588)4037951-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Manin, Jurij I. |d 1937-2023 |e Sonstige |0 (DE-588)121177580 |4 oth | |
| 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 | |
| 856 | 4 | 2 | |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=3264873&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-018703240 | |
Record in the Search Index
| _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 |
| any_adam_object | 1 |
| author_GND | (DE-588)121177580 (DE-588)14102545X |
| building | Verbundindex |
| bvnumber | BV035845025 |
| callnumber-first | Q - Science |
| callnumber-label | QA9 |
| callnumber-raw | QA9 |
| callnumber-search | QA9 |
| callnumber-sort | QA 19 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 130 |
| ctrlnum | (OCoLC)436030792 (DE-599)DNB99339664X |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV035845025</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20180814</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">091125s2010 d||| |||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">09,N15,0642</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">99339664X</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781441906144</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4419-0614-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781441906151</subfield><subfield code="c">ebook</subfield><subfield code="9">978-1-4419-0615-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461424796</subfield><subfield code="9">978-1-4614-2479-6</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9781441906144</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">12617210</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)436030792</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB99339664X</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-521</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA9</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.3</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 130</subfield><subfield code="0">(DE-625)143216:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">03-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">03-XX</subfield><subfield code="2">msc</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A course in mathematical logic for mathematicians</subfield><subfield code="c">Yu. I. Manin</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield><subfield code="b">with new chapters by Boris Zilber and Yuri I. Manin</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVII, 384 S.</subfield><subfield code="b">graph. Darst.</subfield><subfield code="c">235 mm x 155 mm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">53</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Kap. I-VIII aus dem Russ. übers.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Logic, Symbolic and mathematical</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematische Logik</subfield><subfield code="0">(DE-588)4037951-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4151278-9</subfield><subfield code="a">Einführung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Mathematische Logik</subfield><subfield code="0">(DE-588)4037951-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Manin, Jurij I.</subfield><subfield code="d">1937-2023</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)121177580</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zilber, Boris</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)14102545X</subfield><subfield code="4">oth</subfield></datafield><datafield tag="780" ind1="0" ind2="0"><subfield code="i">1. Auflage</subfield><subfield code="a">Manin, Jurij I.</subfield><subfield code="t">A course in mathematical logic</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">53</subfield><subfield code="w">(DE-604)BV000000067</subfield><subfield code="9">53</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="q">text/html</subfield><subfield code="u">http://deposit.dnb.de/cgi-bin/dokserv?id=3264873&prov=M&dok_var=1&dok_ext=htm</subfield><subfield code="3">Inhaltstext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Passau - ADAM Catalogue Enrichment</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-018703240</subfield></datafield></record></collection> |
| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV035845025 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T10:24:19Z |
| institution | BVB |
| isbn | 9781441906144 9781441906151 9781461424796 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018703240 |
| oclc_num | 436030792 |
| open_access_boolean | |
| owner | DE-20 DE-706 DE-384 DE-11 DE-188 DE-83 DE-521 DE-739 DE-355 DE-BY-UBR |
| owner_facet | DE-20 DE-706 DE-384 DE-11 DE-188 DE-83 DE-521 DE-739 DE-355 DE-BY-UBR |
| physical | XVII, 384 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| 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 |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3264873&prov=M&dok_var=1&dok_ext=htm 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 |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT maninjuriji acourseinmathematicallogicformathematicians AT zilberboris acourseinmathematicallogicformathematicians |