Forcing indestructibility of MAD families

Let A [] be a maximal almost disjoint family and assume P is a forcing notion. Say A is P-indestructible if A is still maximal in any P-generic extension. We investigate P-indestructibility for several classical forcing notions P. In particular, we provide a combinatorial characterization of P-indestructibility and, assuming a fragment of MA, we construct maximal almost disjoint families which are P-indestructible yet Q-destructible for several pairs of forcing notions (P, Q). We close with a detailed investigation of iterated Sacks indestructibility.

• Type: Journal
• Year: 2005
• Where: APAL
• Authors: Jörg Brendle, Shunsuke Yatabe
• Keywords: APAL 2005, Classical Forcing Notions, Forcing Notions, P-generic Extension