Coding the universe /:
Axiomatic set theory is the concern of this book. More particularly, the authors prove results about the coding of models M, of Zermelo-Fraenkel set theory together with the Generalized Continuum Hypothesis by using a class 'forcing' construction. By this method they extend M to another mo...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [Cambridgeshire] ; New York :
Cambridge University Press,
©1982.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
47. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Axiomatic set theory is the concern of this book. More particularly, the authors prove results about the coding of models M, of Zermelo-Fraenkel set theory together with the Generalized Continuum Hypothesis by using a class 'forcing' construction. By this method they extend M to another model L[a] with the same properties. L[a] is Gödels universe of 'constructible' sets L, together with a set of integers a which code all the cardinality and cofinality structure of M. Some applications are also considered. Graduate students and research workers in set theory and logic will be especially interested by this account. |
| Beschreibung: | Includes indexes. |
| Beschreibung: | 1 online resource (353 pages) |
| Bibliographie: | Includes bibliographical references (pages 347-348). |
| ISBN: | 9781107361058 1107361052 9780511892042 0511892047 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn839304419 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 130415s1982 enk ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e pn |c N$T |d E7B |d OCLCF |d YDXCP |d OCLCQ |d AGLDB |d OCLCQ |d OCLCO |d UAB |d OCLCQ |d VTS |d REC |d OCLCO |d STF |d AU@ |d OCLCO |d M8D |d OCLCQ |d K6U |d SFB |d OCLCO |d OCLCQ |d OCLCO |d OCLCL |d OCLCQ | ||
| 019 | |a 708564097 | ||
| 020 | |a 9781107361058 |q (electronic bk.) | ||
| 020 | |a 1107361052 |q (electronic bk.) | ||
| 020 | |a 9780511892042 |q (e-book) | ||
| 020 | |a 0511892047 |q (e-book) | ||
| 020 | |z 0521280404 | ||
| 020 | |z 9780521280402 | ||
| 020 | |z 0521280480 | ||
| 035 | |a (OCoLC)839304419 |z (OCoLC)708564097 | ||
| 050 | 4 | |a QA248 |b .B45 1982eb | |
| 072 | 7 | |a MAT |x 028000 |2 bisacsh | |
| 082 | 7 | |a 511.3/22 |2 22 | |
| 084 | |a 31.10 |2 bcl | ||
| 084 | |a SI 320 |2 rvk | ||
| 084 | |a SK 130 |2 rvk | ||
| 049 | |a MAIN | ||
| 100 | 1 | |a Beller, A. | |
| 245 | 1 | 0 | |a Coding the universe / |c A. Beller, R. Jensen, P. Welch. |
| 260 | |a Cambridge [Cambridgeshire] ; |a New York : |b Cambridge University Press, |c ©1982. | ||
| 300 | |a 1 online resource (353 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society lecture note series ; |v 47 | |
| 504 | |a Includes bibliographical references (pages 347-348). | ||
| 500 | |a Includes indexes. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a Axiomatic set theory is the concern of this book. More particularly, the authors prove results about the coding of models M, of Zermelo-Fraenkel set theory together with the Generalized Continuum Hypothesis by using a class 'forcing' construction. By this method they extend M to another model L[a] with the same properties. L[a] is Gödels universe of 'constructible' sets L, together with a set of integers a which code all the cardinality and cofinality structure of M. Some applications are also considered. Graduate students and research workers in set theory and logic will be especially interested by this account. | ||
| 505 | 0 | |a Cover; Title; Copyright; Contents; 0. An introduction; 1. The building blocks; 1.1 The Plan; 1.2 Almost Disjoint Forcing; 1.3 RESHAPING; 1.4 LIMIT CARDINALS; 2. The conditions; 2.1 INTRODUCTION; 2.2 THE RESHAPING CONDITIONS a; 2.3 THE AUXILIARY LEMMAS; 2.4 RS-THE SUCCESSOR STAGE; 2.4.1 Definition 1; 2.4.3 Definition of w :; 2.4.4 Fact; 2.5 THE LIMIT CASE AND PT; 2.6 DEFINITION OF PS and PT T; 2.7 EXTENSION OF CONDITIONS IN P S; 3. Distributivity; 3.1 INTRODUCTION; 3.2 CONSEQUENCES OF THEOREMS 3.1 and 3.2; 3.3 PRELIMINARIES OF THE PROOF OF THEOREMS 3.1 AND 3.2; 3.4 THE LEMMA | |
| 505 | 8 | |a 3.5 THE INACCESSIBLE CASE3.6 THE SINGULAR CASE; 3.7 DISTRIBUTIVITY OF PT; 4. The denouement; 4.2 LARGE CARDINAL FACTS; 4.3 PRESERVATION OF LARGE CARDINALS; 4 . 4 O^AND THEOREM 0 . 2; 5. Applications; 5 . 1 A NEW VERSION OF SOLOVAY'S CONJECTURE; 5.2 DESTROYING COUNTABLE MODELS OF ZF; 5.2.1 Avoiding Inaccessibles; 5.2.2 Destroying Inaccessibles; 5.2.3 Eliminating Singular Cardinal Models of ZF; 5.2.4 Purging the Rest of the ZF Models; 5.2.4.1 New Definition of S; 5.3 FORCING WITH 0^; 6. The fine-structural lemmas; 6.1 AN INTRODUCTION; 6.2 THE LEMMAS; 7. The Cohen-generic sets | |
| 505 | 8 | |a 8. How to get rid of "" 1 0 * ""8.1 M CLOSED UNDER SHARPS; 9. Some further applications; Appendix; Bibliography; Notational index; Index | |
| 650 | 0 | |a Axiomatic set theory. |0 http://id.loc.gov/authorities/subjects/sh85010588 | |
| 650 | 0 | |a Logic, Symbolic and mathematical. |0 http://id.loc.gov/authorities/subjects/sh85078115 | |
| 650 | 6 | |a Théorie axiomatique des ensembles. | |
| 650 | 6 | |a Logique symbolique et mathématique. | |
| 650 | 7 | |a MATHEMATICS |x Set Theory. |2 bisacsh | |
| 650 | 7 | |a Axiomatic set theory |2 fast | |
| 650 | 7 | |a Logic, Symbolic and mathematical |2 fast | |
| 650 | 7 | |a Zermelo-Fraenkel-Axiome |2 gnd |0 http://d-nb.info/gnd/4190747-4 | |
| 650 | 1 | 7 | |a Axiomatische methode. |2 gtt |
| 650 | 1 | 7 | |a Symbolische logica. |2 gtt |
| 700 | 1 | |a Jensen, Ronald Björn. | |
| 700 | 1 | |a Welch, P. | |
| 776 | 0 | 8 | |i Print version: |a Beller, A. |t Coding the universe. |d Cambridge [Cambridgeshire] ; New York : Cambridge University Press, ©1982 |z 9780521280402 |w (DLC) 81002663 |w (OCoLC)7461976 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 47. |0 http://id.loc.gov/authorities/names/n42015587 | |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552384 |3 Volltext |
| 938 | |a ebrary |b EBRY |n ebr10441847 | ||
| 938 | |a EBSCOhost |b EBSC |n 552384 | ||
| 938 | |a YBP Library Services |b YANK |n 10407360 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn839304419 |
|---|---|
| _version_ | 1816882229089927169 |
| adam_text | |
| any_adam_object | |
| author | Beller, A. |
| author2 | Jensen, Ronald Björn Welch, P. |
| author2_role | |
| author2_variant | r b j rb rbj p w pw |
| author_facet | Beller, A. Jensen, Ronald Björn Welch, P. |
| author_role | |
| author_sort | Beller, A. |
| author_variant | a b ab |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA248 |
| callnumber-raw | QA248 .B45 1982eb |
| callnumber-search | QA248 .B45 1982eb |
| callnumber-sort | QA 3248 B45 41982EB |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 320 SK 130 |
| collection | ZDB-4-EBA |
| contents | Cover; Title; Copyright; Contents; 0. An introduction; 1. The building blocks; 1.1 The Plan; 1.2 Almost Disjoint Forcing; 1.3 RESHAPING; 1.4 LIMIT CARDINALS; 2. The conditions; 2.1 INTRODUCTION; 2.2 THE RESHAPING CONDITIONS a; 2.3 THE AUXILIARY LEMMAS; 2.4 RS-THE SUCCESSOR STAGE; 2.4.1 Definition 1; 2.4.3 Definition of w :; 2.4.4 Fact; 2.5 THE LIMIT CASE AND PT; 2.6 DEFINITION OF PS and PT T; 2.7 EXTENSION OF CONDITIONS IN P S; 3. Distributivity; 3.1 INTRODUCTION; 3.2 CONSEQUENCES OF THEOREMS 3.1 and 3.2; 3.3 PRELIMINARIES OF THE PROOF OF THEOREMS 3.1 AND 3.2; 3.4 THE LEMMA 3.5 THE INACCESSIBLE CASE3.6 THE SINGULAR CASE; 3.7 DISTRIBUTIVITY OF PT; 4. The denouement; 4.2 LARGE CARDINAL FACTS; 4.3 PRESERVATION OF LARGE CARDINALS; 4 . 4 O^AND THEOREM 0 . 2; 5. Applications; 5 . 1 A NEW VERSION OF SOLOVAY'S CONJECTURE; 5.2 DESTROYING COUNTABLE MODELS OF ZF; 5.2.1 Avoiding Inaccessibles; 5.2.2 Destroying Inaccessibles; 5.2.3 Eliminating Singular Cardinal Models of ZF; 5.2.4 Purging the Rest of the ZF Models; 5.2.4.1 New Definition of S; 5.3 FORCING WITH 0^; 6. The fine-structural lemmas; 6.1 AN INTRODUCTION; 6.2 THE LEMMAS; 7. The Cohen-generic sets 8. How to get rid of "" 1 0 * ""8.1 M CLOSED UNDER SHARPS; 9. Some further applications; Appendix; Bibliography; Notational index; Index |
| ctrlnum | (OCoLC)839304419 |
| 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 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04728cam a2200709 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn839304419</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cnu---unuuu</controlfield><controlfield tag="008">130415s1982 enk ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">N$T</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">N$T</subfield><subfield code="d">E7B</subfield><subfield code="d">OCLCF</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AGLDB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">UAB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">REC</subfield><subfield code="d">OCLCO</subfield><subfield code="d">STF</subfield><subfield code="d">AU@</subfield><subfield code="d">OCLCO</subfield><subfield code="d">M8D</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">K6U</subfield><subfield code="d">SFB</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield><subfield code="d">OCLCQ</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">708564097</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781107361058</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1107361052</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511892042</subfield><subfield code="q">(e-book)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0511892047</subfield><subfield code="q">(e-book)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">0521280404</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9780521280402</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">0521280480</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)839304419</subfield><subfield code="z">(OCoLC)708564097</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA248</subfield><subfield code="b">.B45 1982eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">028000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">511.3/22</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.10</subfield><subfield code="2">bcl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 320</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 130</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Beller, A.</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Coding the universe /</subfield><subfield code="c">A. Beller, R. Jensen, P. Welch.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Cambridge [Cambridgeshire] ;</subfield><subfield code="a">New York :</subfield><subfield code="b">Cambridge University Press,</subfield><subfield code="c">©1982.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (353 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">London Mathematical Society lecture note series ;</subfield><subfield code="v">47</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 347-348).</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes indexes.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Axiomatic set theory is the concern of this book. More particularly, the authors prove results about the coding of models M, of Zermelo-Fraenkel set theory together with the Generalized Continuum Hypothesis by using a class 'forcing' construction. By this method they extend M to another model L[a] with the same properties. L[a] is Gödels universe of 'constructible' sets L, together with a set of integers a which code all the cardinality and cofinality structure of M. Some applications are also considered. Graduate students and research workers in set theory and logic will be especially interested by this account.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Cover; Title; Copyright; Contents; 0. An introduction; 1. The building blocks; 1.1 The Plan; 1.2 Almost Disjoint Forcing; 1.3 RESHAPING; 1.4 LIMIT CARDINALS; 2. The conditions; 2.1 INTRODUCTION; 2.2 THE RESHAPING CONDITIONS a; 2.3 THE AUXILIARY LEMMAS; 2.4 RS-THE SUCCESSOR STAGE; 2.4.1 Definition 1; 2.4.3 Definition of w :; 2.4.4 Fact; 2.5 THE LIMIT CASE AND PT; 2.6 DEFINITION OF PS and PT T; 2.7 EXTENSION OF CONDITIONS IN P S; 3. Distributivity; 3.1 INTRODUCTION; 3.2 CONSEQUENCES OF THEOREMS 3.1 and 3.2; 3.3 PRELIMINARIES OF THE PROOF OF THEOREMS 3.1 AND 3.2; 3.4 THE LEMMA</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3.5 THE INACCESSIBLE CASE3.6 THE SINGULAR CASE; 3.7 DISTRIBUTIVITY OF PT; 4. The denouement; 4.2 LARGE CARDINAL FACTS; 4.3 PRESERVATION OF LARGE CARDINALS; 4 . 4 O^AND THEOREM 0 . 2; 5. Applications; 5 . 1 A NEW VERSION OF SOLOVAY'S CONJECTURE; 5.2 DESTROYING COUNTABLE MODELS OF ZF; 5.2.1 Avoiding Inaccessibles; 5.2.2 Destroying Inaccessibles; 5.2.3 Eliminating Singular Cardinal Models of ZF; 5.2.4 Purging the Rest of the ZF Models; 5.2.4.1 New Definition of S; 5.3 FORCING WITH 0^; 6. The fine-structural lemmas; 6.1 AN INTRODUCTION; 6.2 THE LEMMAS; 7. The Cohen-generic sets</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">8. How to get rid of "" 1 0 * ""8.1 M CLOSED UNDER SHARPS; 9. Some further applications; Appendix; Bibliography; Notational index; Index</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Axiomatic set theory.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85010588</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Logic, Symbolic and mathematical.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85078115</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Théorie axiomatique des ensembles.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Logique symbolique et mathématique.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Set Theory.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Axiomatic set theory</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Logic, Symbolic and mathematical</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Zermelo-Fraenkel-Axiome</subfield><subfield code="2">gnd</subfield><subfield code="0">http://d-nb.info/gnd/4190747-4</subfield></datafield><datafield tag="650" ind1="1" ind2="7"><subfield code="a">Axiomatische methode.</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1="1" ind2="7"><subfield code="a">Symbolische logica.</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Jensen, Ronald Björn.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Welch, P.</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Beller, A.</subfield><subfield code="t">Coding the universe.</subfield><subfield code="d">Cambridge [Cambridgeshire] ; New York : Cambridge University Press, ©1982</subfield><subfield code="z">9780521280402</subfield><subfield code="w">(DLC) 81002663</subfield><subfield code="w">(OCoLC)7461976</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">London Mathematical Society lecture note series ;</subfield><subfield code="v">47.</subfield><subfield code="0">http://id.loc.gov/authorities/names/n42015587</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552384</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10441847</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">552384</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">10407360</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn839304419 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:17Z |
| institution | BVB |
| isbn | 9781107361058 1107361052 9780511892042 0511892047 |
| language | English |
| oclc_num | 839304419 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (353 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Beller, A. Coding the universe / A. Beller, R. Jensen, P. Welch. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, ©1982. 1 online resource (353 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 47 Includes bibliographical references (pages 347-348). Includes indexes. Print version record. Axiomatic set theory is the concern of this book. More particularly, the authors prove results about the coding of models M, of Zermelo-Fraenkel set theory together with the Generalized Continuum Hypothesis by using a class 'forcing' construction. By this method they extend M to another model L[a] with the same properties. L[a] is Gödels universe of 'constructible' sets L, together with a set of integers a which code all the cardinality and cofinality structure of M. Some applications are also considered. Graduate students and research workers in set theory and logic will be especially interested by this account. Cover; Title; Copyright; Contents; 0. An introduction; 1. The building blocks; 1.1 The Plan; 1.2 Almost Disjoint Forcing; 1.3 RESHAPING; 1.4 LIMIT CARDINALS; 2. The conditions; 2.1 INTRODUCTION; 2.2 THE RESHAPING CONDITIONS a; 2.3 THE AUXILIARY LEMMAS; 2.4 RS-THE SUCCESSOR STAGE; 2.4.1 Definition 1; 2.4.3 Definition of w :; 2.4.4 Fact; 2.5 THE LIMIT CASE AND PT; 2.6 DEFINITION OF PS and PT T; 2.7 EXTENSION OF CONDITIONS IN P S; 3. Distributivity; 3.1 INTRODUCTION; 3.2 CONSEQUENCES OF THEOREMS 3.1 and 3.2; 3.3 PRELIMINARIES OF THE PROOF OF THEOREMS 3.1 AND 3.2; 3.4 THE LEMMA 3.5 THE INACCESSIBLE CASE3.6 THE SINGULAR CASE; 3.7 DISTRIBUTIVITY OF PT; 4. The denouement; 4.2 LARGE CARDINAL FACTS; 4.3 PRESERVATION OF LARGE CARDINALS; 4 . 4 O^AND THEOREM 0 . 2; 5. Applications; 5 . 1 A NEW VERSION OF SOLOVAY'S CONJECTURE; 5.2 DESTROYING COUNTABLE MODELS OF ZF; 5.2.1 Avoiding Inaccessibles; 5.2.2 Destroying Inaccessibles; 5.2.3 Eliminating Singular Cardinal Models of ZF; 5.2.4 Purging the Rest of the ZF Models; 5.2.4.1 New Definition of S; 5.3 FORCING WITH 0^; 6. The fine-structural lemmas; 6.1 AN INTRODUCTION; 6.2 THE LEMMAS; 7. The Cohen-generic sets 8. How to get rid of "" 1 0 * ""8.1 M CLOSED UNDER SHARPS; 9. Some further applications; Appendix; Bibliography; Notational index; Index Axiomatic set theory. http://id.loc.gov/authorities/subjects/sh85010588 Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Théorie axiomatique des ensembles. Logique symbolique et mathématique. MATHEMATICS Set Theory. bisacsh Axiomatic set theory fast Logic, Symbolic and mathematical fast Zermelo-Fraenkel-Axiome gnd http://d-nb.info/gnd/4190747-4 Axiomatische methode. gtt Symbolische logica. gtt Jensen, Ronald Björn. Welch, P. Print version: Beller, A. Coding the universe. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, ©1982 9780521280402 (DLC) 81002663 (OCoLC)7461976 London Mathematical Society lecture note series ; 47. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552384 Volltext |
| spellingShingle | Beller, A. Coding the universe / London Mathematical Society lecture note series ; Cover; Title; Copyright; Contents; 0. An introduction; 1. The building blocks; 1.1 The Plan; 1.2 Almost Disjoint Forcing; 1.3 RESHAPING; 1.4 LIMIT CARDINALS; 2. The conditions; 2.1 INTRODUCTION; 2.2 THE RESHAPING CONDITIONS a; 2.3 THE AUXILIARY LEMMAS; 2.4 RS-THE SUCCESSOR STAGE; 2.4.1 Definition 1; 2.4.3 Definition of w :; 2.4.4 Fact; 2.5 THE LIMIT CASE AND PT; 2.6 DEFINITION OF PS and PT T; 2.7 EXTENSION OF CONDITIONS IN P S; 3. Distributivity; 3.1 INTRODUCTION; 3.2 CONSEQUENCES OF THEOREMS 3.1 and 3.2; 3.3 PRELIMINARIES OF THE PROOF OF THEOREMS 3.1 AND 3.2; 3.4 THE LEMMA 3.5 THE INACCESSIBLE CASE3.6 THE SINGULAR CASE; 3.7 DISTRIBUTIVITY OF PT; 4. The denouement; 4.2 LARGE CARDINAL FACTS; 4.3 PRESERVATION OF LARGE CARDINALS; 4 . 4 O^AND THEOREM 0 . 2; 5. Applications; 5 . 1 A NEW VERSION OF SOLOVAY'S CONJECTURE; 5.2 DESTROYING COUNTABLE MODELS OF ZF; 5.2.1 Avoiding Inaccessibles; 5.2.2 Destroying Inaccessibles; 5.2.3 Eliminating Singular Cardinal Models of ZF; 5.2.4 Purging the Rest of the ZF Models; 5.2.4.1 New Definition of S; 5.3 FORCING WITH 0^; 6. The fine-structural lemmas; 6.1 AN INTRODUCTION; 6.2 THE LEMMAS; 7. The Cohen-generic sets 8. How to get rid of "" 1 0 * ""8.1 M CLOSED UNDER SHARPS; 9. Some further applications; Appendix; Bibliography; Notational index; Index Axiomatic set theory. http://id.loc.gov/authorities/subjects/sh85010588 Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Théorie axiomatique des ensembles. Logique symbolique et mathématique. MATHEMATICS Set Theory. bisacsh Axiomatic set theory fast Logic, Symbolic and mathematical fast Zermelo-Fraenkel-Axiome gnd http://d-nb.info/gnd/4190747-4 Axiomatische methode. gtt Symbolische logica. gtt |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85010588 http://id.loc.gov/authorities/subjects/sh85078115 http://d-nb.info/gnd/4190747-4 |
| title | Coding the universe / |
| title_auth | Coding the universe / |
| title_exact_search | Coding the universe / |
| title_full | Coding the universe / A. Beller, R. Jensen, P. Welch. |
| title_fullStr | Coding the universe / A. Beller, R. Jensen, P. Welch. |
| title_full_unstemmed | Coding the universe / A. Beller, R. Jensen, P. Welch. |
| title_short | Coding the universe / |
| title_sort | coding the universe |
| topic | Axiomatic set theory. http://id.loc.gov/authorities/subjects/sh85010588 Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Théorie axiomatique des ensembles. Logique symbolique et mathématique. MATHEMATICS Set Theory. bisacsh Axiomatic set theory fast Logic, Symbolic and mathematical fast Zermelo-Fraenkel-Axiome gnd http://d-nb.info/gnd/4190747-4 Axiomatische methode. gtt Symbolische logica. gtt |
| topic_facet | Axiomatic set theory. Logic, Symbolic and mathematical. Théorie axiomatique des ensembles. Logique symbolique et mathématique. MATHEMATICS Set Theory. Axiomatic set theory Logic, Symbolic and mathematical Zermelo-Fraenkel-Axiome Axiomatische methode. Symbolische logica. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552384 |
| work_keys_str_mv | AT bellera codingtheuniverse AT jensenronaldbjorn codingtheuniverse AT welchp codingtheuniverse |