Mathematical Research Letters

Volume 5, Issue 2, March 1998 pp. 213-226.

A dichotomy for forcing notions

Authors: Jindrich Zapletal
Author institution: California Institute of Technology

Summary: Let $B$ be Baumgartner's poset for adding a closed unbounded subset of $\omega_1$ with finite conditions. Under the Proper Forcing Axiom, a forcing notion $P$ of size $\aleph_1$ is nowhere c.c.c. if and only if $B$ completely embeds into $P.$

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