The Covering property Axiom, CPA :: a combinatorial core of the iterated perfect set model /
Here the authors formulate and explore a new axiom of set theory, CPA, the Covering Property Axiom. CPA is consistent with the usual ZFC axioms, indeed it is true in the iterated Sacks model and actually captures the combinatorial core of this model. A plethora of results known to be true in the Sac...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, UK ; New York :
Cambridge University Press,
2004.
|
| Schriftenreihe: | Cambridge tracts in mathematics ;
164. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Here the authors formulate and explore a new axiom of set theory, CPA, the Covering Property Axiom. CPA is consistent with the usual ZFC axioms, indeed it is true in the iterated Sacks model and actually captures the combinatorial core of this model. A plethora of results known to be true in the Sacks model easily follow from CPA. Replacing iterated forcing arguments with deductions from CPA simplifies proofs, provides deeper insight, and leads to new results. One may say that CPA is similar in nature to Martin's axiom, as both capture the essence of the models of ZFC in which they hold. The exposition is self contained and there are natural applications to real analysis and topology. Researchers who use set theory in their work will find much of interest in this book. |
| Beschreibung: | 1 online resource (xxi, 174 pages) |
| Bibliographie: | Includes bibliographical references (pages 165-171) and index. |
| ISBN: | 0511212038 9780511212031 0521839203 9780521839204 0511217404 9780511217401 0511215614 9780511215612 0511546459 9780511546457 051131597X 9780511315978 |
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| 505 | 0 | |a 1. Axiom CPA[subscript cube] and its consequences : properties (A)-(E) -- 2. Games and axiom CPA[subscript cube][superscript game] -- 3. Prisms and axioms CPA[subscript prism][superscript game] and CPA[subscript prism] -- 4. CPA[subscript prism] and coverings with smooth functions -- 5. Applications of CPA[subscript prism][superscript game] -- 6. CPA and properties (F[superscript *]) and (G) -- 7. CPA in the Sacks model. | |
| 520 | |a Here the authors formulate and explore a new axiom of set theory, CPA, the Covering Property Axiom. CPA is consistent with the usual ZFC axioms, indeed it is true in the iterated Sacks model and actually captures the combinatorial core of this model. A plethora of results known to be true in the Sacks model easily follow from CPA. Replacing iterated forcing arguments with deductions from CPA simplifies proofs, provides deeper insight, and leads to new results. One may say that CPA is similar in nature to Martin's axiom, as both capture the essence of the models of ZFC in which they hold. The exposition is self contained and there are natural applications to real analysis and topology. Researchers who use set theory in their work will find much of interest in this book. | ||
| 650 | 0 | |a Axiomatic set theory. |0 http://id.loc.gov/authorities/subjects/sh85010588 | |
| 650 | 0 | |a Set theory. |0 http://id.loc.gov/authorities/subjects/sh85120387 | |
| 650 | 6 | |a Théorie axiomatique des ensembles. | |
| 650 | 6 | |a Théorie des ensembles. | |
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Datensatz im Suchindex
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| adam_text | |
| any_adam_object | |
| author | Ciesielski, Krzysztof, 1957- |
| author2 | Pawlikowski, Janusz, 1957- |
| author2_role | |
| author2_variant | j p jp |
| author_GND | http://id.loc.gov/authorities/names/n93095391 http://id.loc.gov/authorities/names/n2004003693 |
| author_facet | Ciesielski, Krzysztof, 1957- Pawlikowski, Janusz, 1957- |
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| contents | 1. Axiom CPA[subscript cube] and its consequences : properties (A)-(E) -- 2. Games and axiom CPA[subscript cube][superscript game] -- 3. Prisms and axioms CPA[subscript prism][superscript game] and CPA[subscript prism] -- 4. CPA[subscript prism] and coverings with smooth functions -- 5. Applications of CPA[subscript prism][superscript game] -- 6. CPA and properties (F[superscript *]) and (G) -- 7. CPA in the Sacks model. |
| ctrlnum | (OCoLC)173610091 |
| 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 |
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Axiom CPA[subscript cube] and its consequences : properties (A)-(E) -- 2. Games and axiom CPA[subscript cube][superscript game] -- 3. Prisms and axioms CPA[subscript prism][superscript game] and CPA[subscript prism] -- 4. CPA[subscript prism] and coverings with smooth functions -- 5. Applications of CPA[subscript prism][superscript game] -- 6. CPA and properties (F[superscript *]) and (G) -- 7. CPA in the Sacks model.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Here the authors formulate and explore a new axiom of set theory, CPA, the Covering Property Axiom. CPA is consistent with the usual ZFC axioms, indeed it is true in the iterated Sacks model and actually captures the combinatorial core of this model. A plethora of results known to be true in the Sacks model easily follow from CPA. Replacing iterated forcing arguments with deductions from CPA simplifies proofs, provides deeper insight, and leads to new results. One may say that CPA is similar in nature to Martin's axiom, as both capture the essence of the models of ZFC in which they hold. The exposition is self contained and there are natural applications to real analysis and topology. 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| genre | Electronic books. |
| genre_facet | Electronic books. |
| id | ZDB-4-EBA-ocn173610091 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:09Z |
| institution | BVB |
| isbn | 0511212038 9780511212031 0521839203 9780521839204 0511217404 9780511217401 0511215614 9780511215612 0511546459 9780511546457 051131597X 9780511315978 |
| language | English |
| oclc_num | 173610091 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xxi, 174 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Cambridge tracts in mathematics ; |
| series2 | Cambridge tracts in mathematics ; |
| spelling | Ciesielski, Krzysztof, 1957- https://id.oclc.org/worldcat/entity/E39PCjFc6FrwMYRdM6FTmMJfVP http://id.loc.gov/authorities/names/n93095391 The Covering property Axiom, CPA : a combinatorial core of the iterated perfect set model / Krzysztof Ciesielski, Janusz Pawlikowski. Cambridge, UK ; New York : Cambridge University Press, 2004. 1 online resource (xxi, 174 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Cambridge tracts in mathematics ; 164 Includes bibliographical references (pages 165-171) and index. Print version record. 1. Axiom CPA[subscript cube] and its consequences : properties (A)-(E) -- 2. Games and axiom CPA[subscript cube][superscript game] -- 3. Prisms and axioms CPA[subscript prism][superscript game] and CPA[subscript prism] -- 4. CPA[subscript prism] and coverings with smooth functions -- 5. Applications of CPA[subscript prism][superscript game] -- 6. CPA and properties (F[superscript *]) and (G) -- 7. CPA in the Sacks model. Here the authors formulate and explore a new axiom of set theory, CPA, the Covering Property Axiom. CPA is consistent with the usual ZFC axioms, indeed it is true in the iterated Sacks model and actually captures the combinatorial core of this model. A plethora of results known to be true in the Sacks model easily follow from CPA. Replacing iterated forcing arguments with deductions from CPA simplifies proofs, provides deeper insight, and leads to new results. One may say that CPA is similar in nature to Martin's axiom, as both capture the essence of the models of ZFC in which they hold. The exposition is self contained and there are natural applications to real analysis and topology. Researchers who use set theory in their work will find much of interest in this book. Axiomatic set theory. http://id.loc.gov/authorities/subjects/sh85010588 Set theory. http://id.loc.gov/authorities/subjects/sh85120387 Théorie axiomatique des ensembles. Théorie des ensembles. MATHEMATICS Set Theory. bisacsh Axiomatic set theory fast Set theory fast Electronic books. Pawlikowski, Janusz, 1957- https://id.oclc.org/worldcat/entity/E39PCjMBChd4yC44vtm8VC8tDm http://id.loc.gov/authorities/names/n2004003693 has work: The Covering property Axiom, CPA (Text) https://id.oclc.org/worldcat/entity/E39PCH44y6KrW79cJRFpv7Brjd https://id.oclc.org/worldcat/ontology/hasWork Print version: Ciesielski, Krzysztof, 1957- Covering property Axiom, CPA. Cambridge, UK ; New York : Cambridge University Press, 2004 (DLC) 2004040788 Cambridge tracts in mathematics ; 164. http://id.loc.gov/authorities/names/n42005726 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=164388 Volltext |
| spellingShingle | Ciesielski, Krzysztof, 1957- The Covering property Axiom, CPA : a combinatorial core of the iterated perfect set model / Cambridge tracts in mathematics ; 1. Axiom CPA[subscript cube] and its consequences : properties (A)-(E) -- 2. Games and axiom CPA[subscript cube][superscript game] -- 3. Prisms and axioms CPA[subscript prism][superscript game] and CPA[subscript prism] -- 4. CPA[subscript prism] and coverings with smooth functions -- 5. Applications of CPA[subscript prism][superscript game] -- 6. CPA and properties (F[superscript *]) and (G) -- 7. CPA in the Sacks model. Axiomatic set theory. http://id.loc.gov/authorities/subjects/sh85010588 Set theory. http://id.loc.gov/authorities/subjects/sh85120387 Théorie axiomatique des ensembles. Théorie des ensembles. MATHEMATICS Set Theory. bisacsh Axiomatic set theory fast Set theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85010588 http://id.loc.gov/authorities/subjects/sh85120387 |
| title | The Covering property Axiom, CPA : a combinatorial core of the iterated perfect set model / |
| title_auth | The Covering property Axiom, CPA : a combinatorial core of the iterated perfect set model / |
| title_exact_search | The Covering property Axiom, CPA : a combinatorial core of the iterated perfect set model / |
| title_full | The Covering property Axiom, CPA : a combinatorial core of the iterated perfect set model / Krzysztof Ciesielski, Janusz Pawlikowski. |
| title_fullStr | The Covering property Axiom, CPA : a combinatorial core of the iterated perfect set model / Krzysztof Ciesielski, Janusz Pawlikowski. |
| title_full_unstemmed | The Covering property Axiom, CPA : a combinatorial core of the iterated perfect set model / Krzysztof Ciesielski, Janusz Pawlikowski. |
| title_short | The Covering property Axiom, CPA : |
| title_sort | covering property axiom cpa a combinatorial core of the iterated perfect set model |
| title_sub | a combinatorial core of the iterated perfect set model / |
| topic | Axiomatic set theory. http://id.loc.gov/authorities/subjects/sh85010588 Set theory. http://id.loc.gov/authorities/subjects/sh85120387 Théorie axiomatique des ensembles. Théorie des ensembles. MATHEMATICS Set Theory. bisacsh Axiomatic set theory fast Set theory fast |
| topic_facet | Axiomatic set theory. Set theory. Théorie axiomatique des ensembles. Théorie des ensembles. MATHEMATICS Set Theory. Axiomatic set theory Set theory Electronic books. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=164388 |
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