Combining Resurrection and Maximality

Abstract

It is shown that the resurrection axiom and the maximality principle may be consistently combined for various iterable forcing classes. The extent to which resurrection and maximality overlap is explored via the local maximality principle.2010 Mathematics Subject Classification. 03E40, 03E55. Key words and phrases. subcomplete forcing, proper forcing, the maximality principle, the resurrection axiom.Some of the material presented here is based on the author's doctoral thesis [Min17], written at the Graduate Center of CUNY under the supervision of Gunter Fuchs.