Two applications of logic to mathematics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ
Princeton Univ. Press
1978
|
| Series: | Kanô memorial lectures.
3. Nihon Sugakkai: Publications of the Mathematical Society of Japan. 13. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 137 S. |
| ISBN: | 069108212X |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV003696991 | ||
| 003 | DE-604 | ||
| 005 | 19960930 | ||
| 007 | t | ||
| 008 | 900725s1978 |||| 00||| eng d | ||
| 020 | |a 069108212X |9 0-691-08212-X | ||
| 035 | |a (OCoLC)438847531 | ||
| 035 | |a (DE-599)BVBBV003696991 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-739 |a DE-91 |a DE-91G |a DE-19 |a DE-29T |a DE-706 |a DE-188 | ||
| 084 | |a SK 130 |0 (DE-625)143216: |2 rvk | ||
| 084 | |a SK 150 |0 (DE-625)143218: |2 rvk | ||
| 100 | 1 | |a Takeuti, Gaisi |d 1926-2017 |e Verfasser |0 (DE-588)107888580 |4 aut | |
| 245 | 1 | 0 | |a Two applications of logic to mathematics |c by Gaisi Takeuti |
| 264 | 1 | |a Princeton, NJ |b Princeton Univ. Press |c 1978 | |
| 300 | |a VIII, 137 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Kanô memorial lectures. |v 3. | |
| 490 | 1 | |a Nihon Sugakkai: Publications of the Mathematical Society of Japan. |v 13. | |
| 650 | 4 | |a logika | |
| 650 | 0 | 7 | |a Mathematische Logik |0 (DE-588)4037951-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Boolesche Algebra |0 (DE-588)4146280-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Analysis |0 (DE-588)4001865-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Boolesche Algebra |0 (DE-588)4146280-4 |D s |
| 689 | 0 | 1 | |a Analysis |0 (DE-588)4001865-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Analysis |0 (DE-588)4001865-9 |D s |
| 689 | 1 | 1 | |a Mathematische Logik |0 (DE-588)4037951-6 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Kanô memorial lectures. |v 3. |w (DE-604)BV002788448 |9 3. | |
| 830 | 0 | |a Nihon Sugakkai: Publications of the Mathematical Society of Japan. |v 13. |w (DE-604)BV001888196 |9 13. | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002353021&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-002353021 | ||
Record in the Search Index
| _version_ | 1804118041630343168 |
|---|---|
| adam_text | Contents
Preface
Introduction 1
Parti
Boolean Valued Analysis
Chapter 1 Boolean Valued Analysis Using Projection Algebras 6
§ 1. Hilbert space 6
§ 2. The model FW 7
§ 3. Real numbers in K J 15
§ 4. The interpretation of elementary theorems 21
§ 5. Miscellaneous interpretations 29
§ 6. Convergence 31
§ 7. Semi group of self adjoint operators 33
§ 8. Complete Boolean algebras of Banach spaces 38
§ 9. Piecewise convergence 40
§10. Simultaneous spectrums 42
§11. Quantum Logic 46
Chapter 2 Boolean Valued Analysis Using Measure Algebras 51
§ 1. Measure algebras 51
§ 2. Real numbers in the model 52
§ 3. Continuous functions in the model 56
§ 4. Baire functions and Borel sets in the model 60
§ 5. Integration and differentiation in the model 63
§ 6. Relation between projection algebras and
measure algebras 68
References 71
Part II
A Conservative Extension of Peano Arithmetic
Chapter 1 Real Analysis 77
§ 1. The first system 77
viii Contents
§ 2. The second system 89
§ 3. Defining reals 91
§ 4. Functions 93
§ 5. Sequences 96
§ 6. Continuous functions 98
§ 7. Differentiation 101
§ 8. Integration 104
§ 9. Sequences of functions 106
§ 10. Infinite series and series of functions 107
§ 11. Higher derivatives 110
§ 12. Functions of several variables 112
Chapter 2 Complex Analysis 114
§ 1. A system of complex numbers 114
§ 2. Analytic functions 119
§ 3. Integration 122
§ 4. Cauchy s Theorem for nice regions 125
§ 5. Cauchy s Integral Formula 127
§ 6. The general form of Cauchy s Theorem 132
§ 7. Miscellaneous remarks 133
§ 8. Final remarks 134
References 136
Index 139
|
| any_adam_object | 1 |
| author | Takeuti, Gaisi 1926-2017 |
| author_GND | (DE-588)107888580 |
| author_facet | Takeuti, Gaisi 1926-2017 |
| author_role | aut |
| author_sort | Takeuti, Gaisi 1926-2017 |
| author_variant | g t gt |
| building | Verbundindex |
| bvnumber | BV003696991 |
| classification_rvk | SK 130 SK 150 |
| ctrlnum | (OCoLC)438847531 (DE-599)BVBBV003696991 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01930nam a2200457 cb4500</leader><controlfield tag="001">BV003696991</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19960930 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">900725s1978 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">069108212X</subfield><subfield code="9">0-691-08212-X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)438847531</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV003696991</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-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-188</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">SK 150</subfield><subfield code="0">(DE-625)143218:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Takeuti, Gaisi</subfield><subfield code="d">1926-2017</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)107888580</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Two applications of logic to mathematics</subfield><subfield code="c">by Gaisi Takeuti</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, NJ</subfield><subfield code="b">Princeton Univ. Press</subfield><subfield code="c">1978</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VIII, 137 S.</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">Kanô memorial lectures.</subfield><subfield code="v">3.</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Nihon Sugakkai: Publications of the Mathematical Society of Japan.</subfield><subfield code="v">13.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">logika</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="650" ind1="0" ind2="7"><subfield code="a">Boolesche Algebra</subfield><subfield code="0">(DE-588)4146280-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Boolesche Algebra</subfield><subfield code="0">(DE-588)4146280-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Mathematische Logik</subfield><subfield code="0">(DE-588)4037951-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Kanô memorial lectures.</subfield><subfield code="v">3.</subfield><subfield code="w">(DE-604)BV002788448</subfield><subfield code="9">3.</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Nihon Sugakkai: Publications of the Mathematical Society of Japan.</subfield><subfield code="v">13.</subfield><subfield code="w">(DE-604)BV001888196</subfield><subfield code="9">13.</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ 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=002353021&sequence=000002&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:BVB01-002353021</subfield></datafield></record></collection> |
| id | DE-604.BV003696991 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:04:00Z |
| institution | BVB |
| isbn | 069108212X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002353021 |
| oclc_num | 438847531 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-739 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-29T DE-706 DE-188 |
| owner_facet | DE-384 DE-703 DE-739 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-29T DE-706 DE-188 |
| physical | VIII, 137 S. |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| series | Kanô memorial lectures. Nihon Sugakkai: Publications of the Mathematical Society of Japan. |
| series2 | Kanô memorial lectures. Nihon Sugakkai: Publications of the Mathematical Society of Japan. |
| spelling | Takeuti, Gaisi 1926-2017 Verfasser (DE-588)107888580 aut Two applications of logic to mathematics by Gaisi Takeuti Princeton, NJ Princeton Univ. Press 1978 VIII, 137 S. txt rdacontent n rdamedia nc rdacarrier Kanô memorial lectures. 3. Nihon Sugakkai: Publications of the Mathematical Society of Japan. 13. logika Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Boolesche Algebra (DE-588)4146280-4 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Boolesche Algebra (DE-588)4146280-4 s Analysis (DE-588)4001865-9 s DE-604 Mathematische Logik (DE-588)4037951-6 s Kanô memorial lectures. 3. (DE-604)BV002788448 3. Nihon Sugakkai: Publications of the Mathematical Society of Japan. 13. (DE-604)BV001888196 13. HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002353021&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Takeuti, Gaisi 1926-2017 Two applications of logic to mathematics Kanô memorial lectures. Nihon Sugakkai: Publications of the Mathematical Society of Japan. logika Mathematische Logik (DE-588)4037951-6 gnd Boolesche Algebra (DE-588)4146280-4 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4146280-4 (DE-588)4001865-9 |
| title | Two applications of logic to mathematics |
| title_auth | Two applications of logic to mathematics |
| title_exact_search | Two applications of logic to mathematics |
| title_full | Two applications of logic to mathematics by Gaisi Takeuti |
| title_fullStr | Two applications of logic to mathematics by Gaisi Takeuti |
| title_full_unstemmed | Two applications of logic to mathematics by Gaisi Takeuti |
| title_short | Two applications of logic to mathematics |
| title_sort | two applications of logic to mathematics |
| topic | logika Mathematische Logik (DE-588)4037951-6 gnd Boolesche Algebra (DE-588)4146280-4 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | logika Mathematische Logik Boolesche Algebra Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002353021&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002788448 (DE-604)BV001888196 |
| work_keys_str_mv | AT takeutigaisi twoapplicationsoflogictomathematics |