Type: Article

MAD families and strategically bounding forcings

Guzmán, Osvaldo, Hrusak, Michael;

Abstract:

Informally, a proper forcing P is strategically bounding if there is a strategy to prove that P is ??-bounding. We prove that certain MAD families are indestructible by strategically bounding forcings. Our motivation for studying this topic is the problem of Roitman: Does d=1 imply a=?1? From this work, it follows that a model of ?1=d<a cannot be obtained by forcing with a strategically bounding forcing over a model of CH. We prove an iteration theorem for strategically bounding forcings.