The Covering Property Axiom, CPA
A Combinatorial Core of the Iterated Perfect Set Model

This book explores a new axiom of set theory, which simplifies proofs, provides deeper insight, and leads to new results.

Krzysztof Ciesielski (Author), Janusz Pawlikowski (Author)

9780521839204, Cambridge University Press

Hardback, published 23 August 2004

198 pages, 3 b/w illus.
22.9 x 15.2 x 1.6 cm, 0.46 kg

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.

1. Axiom CPAcube and its consequences: properties (A)-(E)
2. Games and axiom CPAgame/cube
3. Prisms and axioms CPAgame/prism and CPAprism
4. CPAprism and coverings with smooth functions
5. Applications of CPAgame/prism
6. CPA and properties (F*) and (G)
7. CPA in the Sacks model.

Subject Areas: Set theory [PBCH], Mathematical foundations [PBC]