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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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2004
|
| Series: | Cambridge tracts in mathematics
164 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | 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 |
| Physical Description: | 1 Online-Ressource (xxi, 174 Seiten) |
| ISBN: | 9780511546457 |
| DOI: | 10.1017/CBO9780511546457 |
Staff View
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| 505 | 8 | |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 | ||
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Record in the Search Index
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| author | Ciesielski, Krzysztof 1957- |
| author_GND | (DE-588)143779508 (DE-588)114658878X |
| author_facet | Ciesielski, Krzysztof 1957- |
| author_role | aut |
| author_sort | Ciesielski, Krzysztof 1957- |
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| building | Verbundindex |
| bvnumber | BV043942127 |
| classification_rvk | SK 260 |
| collection | ZDB-20-CBO |
| 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 | (ZDB-20-CBO)CR9780511546457 (OCoLC)704550348 (DE-599)BVBBV043942127 |
| 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 |
| doi_str_mv | 10.1017/CBO9780511546457 |
| format | Electronic eBook |
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| id | DE-604.BV043942127 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511546457 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351097 |
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| physical | 1 Online-Ressource (xxi, 174 Seiten) |
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| publishDate | 2004 |
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| publisher | Cambridge University Press |
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| spelling | Ciesielski, Krzysztof 1957- Verfasser (DE-588)143779508 aut The Covering property Axiom, CPA a combinatorial core of the iterated perfect set model Krzysztof Ciesielski, Janusz Pawlikowski Cambridge Cambridge University Press 2004 1 Online-Ressource (xxi, 174 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 164 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 Pawlikowski, Janusz 1957- Sonstige (DE-588)114658878X oth Erscheint auch als Druck-Ausgabe 978-0-521-83920-4 https://doi.org/10.1017/CBO9780511546457 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Ciesielski, Krzysztof 1957- The Covering property Axiom, CPA a combinatorial core of the iterated perfect set model 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 |
| 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 | the 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 |
| topic_facet | Axiomatic set theory |
| url | https://doi.org/10.1017/CBO9780511546457 |
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