The Covering Property Axiom, CPA: A Combinatorial Core of the Iterated Perfect Set Model [Hardcover]

This book explores a new axiom of set theory, which simplifies proofs, provides deeper insight, and leads to new results.This book explores a new axiom of set theory,CPA, the Covering Property Axiom. CPA is consistent with the usualZFC axioms, indeed it is true in the iterated Sacks model andactually captures the combinatorial core of this model. A plethora ofresults known to be true in the Sacks model easily follow from CPA.Replacing iterated forcing arguments with deductions from CPAsimplifies proofs, provides deeper insight, and leads to new results.Researchers that use set theory in their work will find much of interest in this book.This book explores a new axiom of set theory,CPA, the Covering Property Axiom. CPA is consistent with the usualZFC axioms, indeed it is true in the iterated Sacks model andactually captures the combinatorial core of this model. A plethora ofresults known to be true in the Sacks model easily follow from CPA.Replacing iterated forcing arguments with deductions from CPAsimplifies proofs, provides deeper insight, and leads to new results.Researchers that use set theory in their work will find much of interest in this book.This book explores a new axiom of set theory--CPA, the Covering Property Axiom. CPA is consistent with the usual ZFC axioms. 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 CPAs simplifies proofs, provides deeper insight, and leads to new results. 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.