TY  - BOOK
AU  - Ciesielski,Krzysztof
AU  - Pawlikowski,Janusz
TI  - The Covering property Axiom, CPA: a combinatorial core of the iterated perfect set model 
T2  - Cambridge tracts in mathematics
SN  - 9780511546457 (ebook)
AV  - QA248 .C473 2004
U1  - 511.3/22 22
PY  - 2004///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Axiomatic set theory
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); 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
N2  - 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
UR  - https://doi.org/10.1017/CBO9780511546457
ER  -