Strongly uplifting cardinals and the boldface resurrection axioms
  We introduce the strongly uplifting cardinals, which are equivalently characterized, we prove, as the superstrongly unfoldable cardinals and also as the almost hugely unfoldable cardinals, and we show that their existence is equiconsistent over ZFC with natural instances of the boldface resurrection axiom, such as the boldface resurrection axiom for proper forcing. 
Joel David Hamkins and Thomas A. Johnstone
math.LO