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The Covering Property Axiom, CPA

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

$124.95

Part of Cambridge Tracts in Mathematics

  • Date Published: August 2004
  • availability: Available
  • format: Hardback
  • isbn: 9780521839204

$ 124.95
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About the Authors
  • 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.

    • Self contained exposition of a new axiom
    • Applications to other parts of mathematics such as real analysis and topology
    • Simple proofs without using forcing
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    Product details

    • Date Published: August 2004
    • format: Hardback
    • isbn: 9780521839204
    • length: 198 pages
    • dimensions: 229 x 152 x 16 mm
    • weight: 0.46kg
    • contains: 3 b/w illus.
    • availability: Available
  • Table of Contents

    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.

  • Authors

    Krzysztof Ciesielski, West Virginia University
    Krzysztof Ciesielski is Professor of Mathematics at West Virginia University.

    Janusz Pawlikowski, Uniwersytet Wroclawski, Poland
    Janusz Pawlikowksi is Professor of Mathematics at Wroclaw University.

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