The Covering Property Axiom, CPA

A Combinatorial Core of the Iterated Perfect Set Model

Krzysztof Ciesielski, Janusz Pawlikowski - Collection Cambridge Tracts in Mathematics

174 pages, parution le 03/11/2004

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Résumé

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.

Sommaire

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

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Krzysztof Ciesielski, Janusz Pawlikowski
Collection	Cambridge Tracts in Mathematics
Parution	03/11/2004
Nb. de pages	174
Format	16 x 23,5
Couverture	Relié
Poids	404g
Intérieur	Noir et Blanc
EAN13	9780521839204
ISBN13	978-0-521-83920-4