Introduction to cardinal arithmetic:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
1999
|
| Series: | Birkhäuser advanced texts : Basler Lehrbücher
Modern Birkhäuser classics |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 304 S. |
| ISBN: | 9783034603270 3764361247 0817661247 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV012707687 | ||
| 003 | DE-604 | ||
| 005 | 20180905 | ||
| 007 | t | ||
| 008 | 990803s1999 gw |||| 00||| eng d | ||
| 020 | |a 9783034603270 |9 978-3-0346-0327-0 | ||
| 020 | |a 3764361247 |c (Basel ...) Kunststoff : sfr 88.00 |9 3-7643-6124-7 | ||
| 020 | |a 0817661247 |c (Boston) Kunststoff |9 0-8176-6124-7 | ||
| 035 | |a (OCoLC)41674408 | ||
| 035 | |a (DE-599)BVBBV012707687 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-739 |a DE-824 |a DE-20 |a DE-355 |a DE-91G |a DE-634 |a DE-384 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA248 | |
| 082 | 0 | |a 511.3/22 |2 21 | |
| 084 | |a CC 2600 |0 (DE-625)17610: |2 rvk | ||
| 084 | |a SK 150 |0 (DE-625)143218: |2 rvk | ||
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a MAT 100f |2 stub | ||
| 100 | 1 | |a Holz, Michael |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to cardinal arithmetic |c M. Holz ; K. Steffens ; E. Weitz |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1999 | |
| 300 | |a VI, 304 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Birkhäuser advanced texts : Basler Lehrbücher | |
| 490 | 0 | |a Modern Birkhäuser classics | |
| 650 | 7 | |a Arithmétique |2 ram | |
| 650 | 7 | |a Géométrie algébrique arithmétique |2 ram | |
| 650 | 4 | |a Cardinal numbers | |
| 650 | 0 | 7 | |a Kardinalzahl |0 (DE-588)4163318-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kardinalzahl |0 (DE-588)4163318-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Steffens, Karsten |e Verfasser |4 aut | |
| 700 | 1 | |a Weitz, Edmund |d 1965- |e Verfasser |0 (DE-588)116625559X |4 aut | |
| 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=008638183&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-008638183 | ||
Record in the Search Index
| _version_ | 1804127370699866112 |
|---|---|
| adam_text | Contents
Preface vii
Introduction 1
1 Foundations
1.1 The Axioms of ZFC 5
1.2 Ordinals 15
1.3 Transfinite Induction and Recursion 20
1.4 Arithmetic of Ordinals 30
1.5 Cardinal Numbers and their Elementary Properties 40
1.6 Infinite Sums and Products 58
1.7 Further Properties of kx the Singular Cardinal Hypothesis . . 70
1.8 Clubs and Stationary Sets 79
1.9 The Erdos Rado Partition Theorem 96
2 The Galvin Hajnal Theorem
2.1 Ideals and the Reduction of Relations 103
2.2 The Galvin Hajnal Formula 108
2.3 Applications of the Galvin Hajnal Formula 121
3 Ordinal Functions
3.1 Suprema and Cofinalities 131
3.2 K rapid Sequences and the Main Lemma of pcf Theory 143
3.3 The Definition and Simple Properties of pcf(a) 151
3.4 The Ideal J A(a) 159
4 Approximation Sequences
4.1 The Sets H(0) 173
4.2 Models and Absoluteness 176
4.3 Approximation Sequences 196
4.4 The Skolem Hull in H(9) 199
4.5 O Club Sequences 202
vi Contents
5 Generators of »T a+ (a)
5.1 Universal Sequences 209
5.2 The Existence of Generators 213
5.3 Properties of Generators 218
6 The Supremum of pcfM (a)
6.1 Control Functions 221
6.2 The Supremum of pcf/i(a) 225
7 Local Properties
7.1 The Ideals «7,(b) and J|A(a) 233
7.2 Intervals in pcf(a) 244
8 Applications of pcf Theory
8.1 Cardinal Estimates 249
8.2 Jonsson Algebras 251
8.3 A Partition Theorem of Todorcevic 262
8.4 Cofinalities of Partial Orderings ([A]^K,C) 265
9 The Cardinal Function pp(A)
9.1 pp(A) and the Theorems of Galvin, Hajnal and Silver 270
9.2 The Lemma of Galvin and Hajnal for pp(A) 275
Bibliography 287
List of Symbols 289
Index 293
|
| any_adam_object | 1 |
| author | Holz, Michael Steffens, Karsten Weitz, Edmund 1965- |
| author_GND | (DE-588)116625559X |
| author_facet | Holz, Michael Steffens, Karsten Weitz, Edmund 1965- |
| author_role | aut aut aut |
| author_sort | Holz, Michael |
| author_variant | m h mh k s ks e w ew |
| building | Verbundindex |
| bvnumber | BV012707687 |
| callnumber-first | Q - Science |
| callnumber-label | QA248 |
| callnumber-raw | QA248 |
| callnumber-search | QA248 |
| callnumber-sort | QA 3248 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | CC 2600 SK 150 SK 180 |
| classification_tum | MAT 100f |
| ctrlnum | (OCoLC)41674408 (DE-599)BVBBV012707687 |
| dewey-full | 511.3/22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/22 |
| dewey-search | 511.3/22 |
| dewey-sort | 3511.3 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01898nam a2200493 c 4500</leader><controlfield tag="001">BV012707687</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20180905 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">990803s1999 gw |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783034603270</subfield><subfield code="9">978-3-0346-0327-0</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3764361247</subfield><subfield code="c">(Basel ...) Kunststoff : sfr 88.00</subfield><subfield code="9">3-7643-6124-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0817661247</subfield><subfield code="c">(Boston) Kunststoff</subfield><subfield code="9">0-8176-6124-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)41674408</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV012707687</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="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-739</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA248</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.3/22</subfield><subfield code="2">21</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 150</subfield><subfield code="0">(DE-625)143218:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 100f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Holz, Michael</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Introduction to cardinal arithmetic</subfield><subfield code="c">M. Holz ; K. Steffens ; E. Weitz</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Basel [u.a.]</subfield><subfield code="b">Birkhäuser</subfield><subfield code="c">1999</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VI, 304 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="0" ind2=" "><subfield code="a">Birkhäuser advanced texts : Basler Lehrbücher</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Modern Birkhäuser classics</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Arithmétique</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Géométrie algébrique arithmétique</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Cardinal numbers</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kardinalzahl</subfield><subfield code="0">(DE-588)4163318-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Kardinalzahl</subfield><subfield code="0">(DE-588)4163318-0</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">Steffens, Karsten</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Weitz, Edmund</subfield><subfield code="d">1965-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)116625559X</subfield><subfield code="4">aut</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=008638183&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:BVB01-008638183</subfield></datafield></record></collection> |
| id | DE-604.BV012707687 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:32:16Z |
| institution | BVB |
| isbn | 9783034603270 3764361247 0817661247 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008638183 |
| oclc_num | 41674408 |
| open_access_boolean | |
| owner | DE-739 DE-824 DE-20 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-634 DE-384 DE-11 DE-188 |
| owner_facet | DE-739 DE-824 DE-20 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-634 DE-384 DE-11 DE-188 |
| physical | VI, 304 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Birkhäuser advanced texts : Basler Lehrbücher Modern Birkhäuser classics |
| spelling | Holz, Michael Verfasser aut Introduction to cardinal arithmetic M. Holz ; K. Steffens ; E. Weitz Basel [u.a.] Birkhäuser 1999 VI, 304 S. txt rdacontent n rdamedia nc rdacarrier Birkhäuser advanced texts : Basler Lehrbücher Modern Birkhäuser classics Arithmétique ram Géométrie algébrique arithmétique ram Cardinal numbers Kardinalzahl (DE-588)4163318-0 gnd rswk-swf Kardinalzahl (DE-588)4163318-0 s DE-604 Steffens, Karsten Verfasser aut Weitz, Edmund 1965- Verfasser (DE-588)116625559X aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008638183&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Holz, Michael Steffens, Karsten Weitz, Edmund 1965- Introduction to cardinal arithmetic Arithmétique ram Géométrie algébrique arithmétique ram Cardinal numbers Kardinalzahl (DE-588)4163318-0 gnd |
| subject_GND | (DE-588)4163318-0 |
| title | Introduction to cardinal arithmetic |
| title_auth | Introduction to cardinal arithmetic |
| title_exact_search | Introduction to cardinal arithmetic |
| title_full | Introduction to cardinal arithmetic M. Holz ; K. Steffens ; E. Weitz |
| title_fullStr | Introduction to cardinal arithmetic M. Holz ; K. Steffens ; E. Weitz |
| title_full_unstemmed | Introduction to cardinal arithmetic M. Holz ; K. Steffens ; E. Weitz |
| title_short | Introduction to cardinal arithmetic |
| title_sort | introduction to cardinal arithmetic |
| topic | Arithmétique ram Géométrie algébrique arithmétique ram Cardinal numbers Kardinalzahl (DE-588)4163318-0 gnd |
| topic_facet | Arithmétique Géométrie algébrique arithmétique Cardinal numbers Kardinalzahl |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008638183&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT holzmichael introductiontocardinalarithmetic AT steffenskarsten introductiontocardinalarithmetic AT weitzedmund introductiontocardinalarithmetic |