The Covering property Axiom, CPA : a combinatorial core of the iterated perfect set model /
Ciesielski, Krzysztof, 1957-
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) - Cambridge tracts in mathematics ; 164 . - Cambridge tracts in mathematics ; 164. .
Includes bibliographical references (pages 165-171) and index.
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.
0511212038 9780511212031 0521839203 9780521839204 0511217404 (electronic bk.) 9780511217401 (electronic bk.) 0511215614 (electronic bk.) 9780511215612 (electronic bk.) 0511546459 (electronic book) 9780511546457 (electronic book) 051131597X (e-book) 9780511315978 (e-book)
2004040788
013021304. Uk
Axiomatic set theory.
Set theory.
Théorie axiomatique des ensembles.
Théorie des ensembles.
MATHEMATICS--Set Theory.
Axiomatic set theory.
Set theory.
Electronic books.
Electronic books.
Electronic books.
QA248 / .C473 2004eb
511.3/22
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) - Cambridge tracts in mathematics ; 164 . - Cambridge tracts in mathematics ; 164. .
Includes bibliographical references (pages 165-171) and index.
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.
0511212038 9780511212031 0521839203 9780521839204 0511217404 (electronic bk.) 9780511217401 (electronic bk.) 0511215614 (electronic bk.) 9780511215612 (electronic bk.) 0511546459 (electronic book) 9780511546457 (electronic book) 051131597X (e-book) 9780511315978 (e-book)
2004040788
013021304. Uk
Axiomatic set theory.
Set theory.
Théorie axiomatique des ensembles.
Théorie des ensembles.
MATHEMATICS--Set Theory.
Axiomatic set theory.
Set theory.
Electronic books.
Electronic books.
Electronic books.
QA248 / .C473 2004eb
511.3/22