E-grāmata: Covering Property Axiom, CPA: A Combinatorial Core of the Iterated Perfect Set Model

Mathematicians Ciesielski (West Virginia U.) and Pawlikowski (Wroclaw U.) present a new axiom of set theory they call the Covering Property Axiom, CPA, and show how it is consistent with the usual ZFC axioms, and is not only true in the iterated perfect set Sacks model but actually captures its combinatorial core. Many results known to be true in the Sack model easily follow from their Axiom, they say, and the iterated forcing arguments are replaced with deductions, which simplified proofs, provides deeper insight, and leads to new results. Annotation ©2005 Book News, Inc., Portland, OR (booknews.com)

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 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.