Fundamentals of mathematical logic:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Wellesley, Mass.
A. K. Peters
2005
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 878 S. graph. Darst. |
| ISBN: | 1568812620 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV021290008 | ||
| 003 | DE-604 | ||
| 005 | 20100202 | ||
| 007 | t | ||
| 008 | 060112s2005 xxud||| |||| 00||| eng d | ||
| 020 | |a 1568812620 |9 1-56881-262-0 | ||
| 035 | |a (OCoLC)60796293 | ||
| 035 | |a (DE-599)BVBBV021290008 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c XD-US | ||
| 049 | |a DE-19 |a DE-521 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA9.H527 2005 | |
| 082 | 0 | |a 511.3 22 | |
| 082 | 0 | |a 511.3 |2 22 | |
| 084 | |a CC 2600 |0 (DE-625)17610: |2 rvk | ||
| 084 | |a SK 130 |0 (DE-625)143216: |2 rvk | ||
| 100 | 1 | |a Hinman, Peter G. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fundamentals of mathematical logic |c Peter G. Hinman |
| 264 | 1 | |a Wellesley, Mass. |b A. K. Peters |c 2005 | |
| 300 | |a XVI, 878 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Lógica matemática (textos avançados) |2 larpcal | |
| 650 | 7 | |a Wiskundige logica |2 gtt | |
| 650 | 4 | |a Logic, Symbolic and mathematical | |
| 650 | 4 | |a Model theory | |
| 650 | 4 | |a Set theory | |
| 650 | 4 | |a Recursion theory | |
| 650 | 0 | 7 | |a Mathematische Logik |0 (DE-588)4037951-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mathematische Logik |0 (DE-588)4037951-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014610869&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-014610869 | ||
Record in the Search Index
| _version_ | 1804135081571254272 |
|---|---|
| adam_text | FUNDAMENTALS OF MATHEMATICAL LOGIC PETER G. HINMAN UNIVERSITY OF
MICHIGAN A K PETERS WELLESLEY, MASSACHUSETTS CONTENTS PREFACE XI
INTRODUCTION 1 1. PROPOSITIONAL LOGIC AND OTHER FUNDAMENTALS . . . .
13 1.1. THE PROPOSITIONAL LANGUAGE 13 1.2. INDUCTION AND RECURSION 20
INDUCTION 20 RECURSION 25 1.3. PROPOSITIONAL SEMANTICS 32 1.4.
PROPOSITIONAL THEORIES 41 GENERAL PROPERTIES 42 COMPACTNESS 47 1.5.
DECIDABILITY AND EFFECTIVE ENUMERABILITY 54 1.6. OTHER CONSTRUCTIONS 63
NOTIONS OF CONSISTENCY 63 ULTRAPRODUCTS 67 1.7. TOPOLOGY AND BOOLEAN
ALGEBRA .72 TOPOLOGY 73 BOOLEAN ALGEBRA 74 VIII CONTENTS 2. FIRST-ORDER
LOGIC 83 2.1. SYNTAX AND SEMANTICS OF FIRST-ORDER LANGUAGES 83 2.2.
BASIC SEMANTICS 96 SUBSTITUTION 105 2.3. STRUCTURES 114 ISOMORPHISM AND
EQUIVALENCE 115 SUBSTRUCTURES 119 PRODUCTS AND CHAINS 130 2.4. THEORIES
139 THE LANGUAGE OF EQUALITY 149 DENSE LINEAR ORDERINGS 154 2.5.
ARITHMETIC 160 2.6. CHANGING LANGUAGES 173 INTERPRETATIONS 186 3.
COMPLETENESS AND COMPACTNESS 193 3.1. COUNTABLE COMPACTNESS 194 3.2.
COUNTABLE COMPLETENESS 204 3.3. OTHER CONSTRUCTIONS 216 NOTIONS OF
CONSISTENCY 216 ULTRAPRODUCTS 224 BOOLEAN ALGEBRA 228 3.4. UNCOUNTABLE
LANGUAGES AND STRUCTURES 236 3.5. APPLICATIONS OF COMPACTNESS 249 3.6.
HIGHER-ORDER LOGIC 276 MONADIC SECOND-ORDER LOGIC 276 3.7. INFINITARY
LOGIC 293 4. INCOMPLETENESS AND UNDECIDABILITY 309 4.1. A FIRST LOOK 310
4.2. RECURSIVE FUNCTIONS AND RELATIONS 326 4.3. RECURSIVELY ENUMERABLE
SETS AND RELATIONS 341 4.4. GODEL NUMBERING . . 352 4.5. DEFINABILITY IN
ARITHMETIC I 364 4.6. REPRESENTABILITY: FIRST INCOMPLETENESS THEOREM 369
5. TOPICS IN DEFINABILITY 393 5.1. DEFINABILITY IN ARITHMETIC II 393
5.2. INDEXING 409 5.3. SECOND INCOMPLETENESS THEOREM 421 CONTENTS IX
5.4. CHURCH S THESIS 431 RECURSION EQUATIONS 432 ABSTRACT MACHINES 436
5.5. APPLICATIONS TO OTHER LANGUAGES AND THEORIES 443 6. SET THEORY 455
6.1. ZERMELO-FRAENKEL SET THEORY 456 6.2. MATHEMATICS IN SET THEORY I
472 6.3. ORDINAL NUMBERS: INDUCTION AND RECURSION 497 6.4. CARDINAL
NUMBERS 510 6.5. MODELS AND INDEPENDENCE 527 6.6. MATHEMATICS IN SET
THEORY II 550 6.7. THE CONSTRUCTIBLE UNIVERSE 567 6.8. GENERIC
EXTENSIONS 577 6.9. FORCING 596 6.10. LARGE CARDINALS 605 6.11.
DETERMINACY 622 7. MODEL THEORY 655 7.1. PARTIAL EMBEDDINGS 655 7.2.
BOOLEAN ALGEBRAS, ULTRAFILTERS AND TYPES 671 7.3. COUNTABLE MODELS OF
COUNTABLE THEORIES 683 7.4. UNCOUNTABLE MODELS OF COUNTABLE THEORIES 700
7.5. MORLEY S THEOREM 708 7.6. ABSTRACT LOGICS 721 8. RECURSION THEORY
733 8.1. MANY-ONE DEGREES AND R.E. SETS 733 8.2. TURING REDUCIBILITY 756
8.3. THE JUMP OPERATOR 770 8.4. UPPER BOUNDS 783 8.5. JUMPS OF R.E. SETS
793 8.6. LOWER BOUNDS 808 REFERENCES 821 ITEM REFERENCES 829 SYMBOL
INDEX 835 SUBJECT INDEX 855
|
| adam_txt |
FUNDAMENTALS OF MATHEMATICAL LOGIC PETER G. HINMAN UNIVERSITY OF
MICHIGAN A K PETERS WELLESLEY, MASSACHUSETTS CONTENTS PREFACE XI
INTRODUCTION 1 1. PROPOSITIONAL LOGIC AND OTHER FUNDAMENTALS . . . .
13 1.1. THE PROPOSITIONAL LANGUAGE 13 1.2. INDUCTION AND RECURSION 20
INDUCTION 20 RECURSION 25 1.3. PROPOSITIONAL SEMANTICS 32 1.4.
PROPOSITIONAL THEORIES 41 GENERAL PROPERTIES 42 COMPACTNESS 47 1.5.
DECIDABILITY AND EFFECTIVE ENUMERABILITY 54 1.6. OTHER CONSTRUCTIONS 63
NOTIONS OF CONSISTENCY 63 ULTRAPRODUCTS 67 1.7. TOPOLOGY AND BOOLEAN
ALGEBRA .72 TOPOLOGY 73 BOOLEAN ALGEBRA 74 VIII CONTENTS 2. FIRST-ORDER
LOGIC 83 2.1. SYNTAX AND SEMANTICS OF FIRST-ORDER LANGUAGES 83 2.2.
BASIC SEMANTICS 96 SUBSTITUTION 105 2.3. STRUCTURES 114 ISOMORPHISM AND
EQUIVALENCE 115 SUBSTRUCTURES 119 PRODUCTS AND CHAINS 130 2.4. THEORIES
139 THE LANGUAGE OF EQUALITY 149 DENSE LINEAR ORDERINGS 154 2.5.
ARITHMETIC 160 2.6. CHANGING LANGUAGES 173 INTERPRETATIONS 186 3.
COMPLETENESS AND COMPACTNESS 193 3.1. COUNTABLE COMPACTNESS 194 3.2.
COUNTABLE COMPLETENESS 204 3.3. OTHER CONSTRUCTIONS 216 NOTIONS OF
CONSISTENCY 216 ULTRAPRODUCTS 224 BOOLEAN ALGEBRA 228 3.4. UNCOUNTABLE
LANGUAGES AND STRUCTURES 236 3.5. APPLICATIONS OF COMPACTNESS 249 3.6.
HIGHER-ORDER LOGIC 276 MONADIC SECOND-ORDER LOGIC 276 3.7. INFINITARY
LOGIC 293 4. INCOMPLETENESS AND UNDECIDABILITY 309 4.1. A FIRST LOOK 310
4.2. RECURSIVE FUNCTIONS AND RELATIONS 326 4.3. RECURSIVELY ENUMERABLE
SETS AND RELATIONS 341 4.4. GODEL NUMBERING . . 352 4.5. DEFINABILITY IN
ARITHMETIC I 364 4.6. REPRESENTABILITY: FIRST INCOMPLETENESS THEOREM 369
5. TOPICS IN DEFINABILITY 393 5.1. DEFINABILITY IN ARITHMETIC II 393
5.2. INDEXING 409 5.3. SECOND INCOMPLETENESS THEOREM 421 CONTENTS IX
5.4. CHURCH'S THESIS 431 RECURSION EQUATIONS 432 ABSTRACT MACHINES 436
5.5. APPLICATIONS TO OTHER LANGUAGES AND THEORIES 443 6. SET THEORY 455
6.1. ZERMELO-FRAENKEL SET THEORY 456 6.2. MATHEMATICS IN SET THEORY I
472 6.3. ORDINAL NUMBERS: INDUCTION AND RECURSION 497 6.4. CARDINAL
NUMBERS 510 6.5. MODELS AND INDEPENDENCE 527 6.6. MATHEMATICS IN SET
THEORY II 550 6.7. THE CONSTRUCTIBLE UNIVERSE 567 6.8. GENERIC
EXTENSIONS 577 6.9. FORCING 596 6.10. LARGE CARDINALS 605 6.11.
DETERMINACY 622 7. MODEL THEORY 655 7.1. PARTIAL EMBEDDINGS 655 7.2.
BOOLEAN ALGEBRAS, ULTRAFILTERS AND TYPES 671 7.3. COUNTABLE MODELS OF
COUNTABLE THEORIES 683 7.4. UNCOUNTABLE MODELS OF COUNTABLE THEORIES 700
7.5. MORLEY'S THEOREM 708 7.6. ABSTRACT LOGICS 721 8. RECURSION THEORY
733 8.1. MANY-ONE DEGREES AND R.E. SETS 733 8.2. TURING REDUCIBILITY 756
8.3. THE JUMP OPERATOR 770 8.4. UPPER BOUNDS 783 8.5. JUMPS OF R.E. SETS
793 8.6. LOWER BOUNDS 808 REFERENCES 821 ITEM REFERENCES 829 SYMBOL
INDEX 835 SUBJECT INDEX 855 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Hinman, Peter G. |
| author_facet | Hinman, Peter G. |
| author_role | aut |
| author_sort | Hinman, Peter G. |
| author_variant | p g h pg pgh |
| building | Verbundindex |
| bvnumber | BV021290008 |
| callnumber-first | Q - Science |
| callnumber-label | QA9 |
| callnumber-raw | QA9.H527 2005 |
| callnumber-search | QA9.H527 2005 |
| callnumber-sort | QA 19 H527 42005 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | CC 2600 SK 130 |
| ctrlnum | (OCoLC)60796293 (DE-599)BVBBV021290008 |
| dewey-full | 511.322 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 22 511.3 |
| dewey-search | 511.3 22 511.3 |
| dewey-sort | 3511.3 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| discipline_str_mv | Mathematik Philosophie |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01571nam a2200445 c 4500</leader><controlfield tag="001">BV021290008</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20100202 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">060112s2005 xxud||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1568812620</subfield><subfield code="9">1-56881-262-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)60796293</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV021290008</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">XD-US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield><subfield code="a">DE-521</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA9.H527 2005</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.3 22</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">CC 2600</subfield><subfield code="0">(DE-625)17610:</subfield><subfield code="2">rvk</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="100" ind1="1" ind2=" "><subfield code="a">Hinman, Peter G.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Fundamentals of mathematical logic</subfield><subfield code="c">Peter G. Hinman</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Wellesley, Mass.</subfield><subfield code="b">A. K. Peters</subfield><subfield code="c">2005</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 878 S.</subfield><subfield code="b">graph. Darst.</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="650" ind1=" " ind2="7"><subfield code="a">Lógica matemática (textos avançados)</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Wiskundige logica</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Logic, Symbolic and mathematical</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Model theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Set theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Recursion theory</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="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="856" ind1="4" ind2="2"><subfield code="m">GBV Datenaustausch</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=014610869&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-014610869</subfield></datafield></record></collection> |
| id | DE-604.BV021290008 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:49:34Z |
| indexdate | 2024-07-09T20:34:50Z |
| institution | BVB |
| isbn | 1568812620 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014610869 |
| oclc_num | 60796293 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-521 DE-11 DE-188 |
| owner_facet | DE-19 DE-BY-UBM DE-521 DE-11 DE-188 |
| physical | XVI, 878 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | A. K. Peters |
| record_format | marc |
| spelling | Hinman, Peter G. Verfasser aut Fundamentals of mathematical logic Peter G. Hinman Wellesley, Mass. A. K. Peters 2005 XVI, 878 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lógica matemática (textos avançados) larpcal Wiskundige logica gtt Logic, Symbolic and mathematical Model theory Set theory Recursion theory Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014610869&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hinman, Peter G. Fundamentals of mathematical logic Lógica matemática (textos avançados) larpcal Wiskundige logica gtt Logic, Symbolic and mathematical Model theory Set theory Recursion theory Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 |
| title | Fundamentals of mathematical logic |
| title_auth | Fundamentals of mathematical logic |
| title_exact_search | Fundamentals of mathematical logic |
| title_exact_search_txtP | Fundamentals of mathematical logic |
| title_full | Fundamentals of mathematical logic Peter G. Hinman |
| title_fullStr | Fundamentals of mathematical logic Peter G. Hinman |
| title_full_unstemmed | Fundamentals of mathematical logic Peter G. Hinman |
| title_short | Fundamentals of mathematical logic |
| title_sort | fundamentals of mathematical logic |
| topic | Lógica matemática (textos avançados) larpcal Wiskundige logica gtt Logic, Symbolic and mathematical Model theory Set theory Recursion theory Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Lógica matemática (textos avançados) Wiskundige logica Logic, Symbolic and mathematical Model theory Set theory Recursion theory Mathematische Logik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014610869&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hinmanpeterg fundamentalsofmathematicallogic |