Resurrection axioms and uplifting cardinals

We introduce the resurrection axioms, a new class of forcing axioms, and the uplifting cardinals, a new large cardinal notion, and prove that various instances of the resurrection axioms are equiconsistent over ZFC with the existence of an uplifting cardinal.

[1]  Thomas A. Johnstone.  Strongly unfoldable cardinals made indestructible , 2008, Journal of Symbolic Logic.

[2]  Joel David Hamkins,et al.  Diamond (on the regulars) can fail at any strongly unfoldable cardinal , 2006, Ann. Pure Appl. Log..

[3]  Joel David Hamkins.  The Lottery Preparation , 2000, Ann. Pure Appl. Log..

[4]  Richard Laver,et al.  Making the supercompactness of κ indestructible under κ-directed closed forcing , 1978 .

[5]  Jouko Väänänen,et al.  Reflection principles for the continuum , 2008 .

[6]  Tadatoshi Miyamoto.  A Note on Weak Segments of PFA , 1998 .

[7]  Joel David Hamkins,et al.  Indestructible Strong Unfoldability , 2010, Notre Dame J. Formal Log..

[8]  Jonas Reitz.  The ground axiom , 2007, J. Symb. Log..

[9]  Saharon Shelah,et al.  Forcing closed unbounded sets , 1983, Journal of Symbolic Logic.

[10]  JOEL DAVID HAMKINS,et al.  Generalizations of the Kunen inconsistency , 2012, Ann. Pure Appl. Log..

[12]  Joan Bagaria.  A Characterization of Martin's Axiom in Terms of Absoluteness , 1997, J. Symb. Log..

[13]  Andrés Villaveces.  Chains of End Elementary Extensions of Models of Set Theory , 1998, J. Symb. Log..

[14]  Piotr Koszmider.  On Coherent Families of Finite-to-One Functions , 1993, J. Symb. Log..

[15]  Saharon Shelah,et al.  The Bounded Proper Forcing Axiom , 1995, J. Symb. Log..

[17]  Joel David Hamkins.  A class of strong diamond principles , 2002 .

[18]  Joan Bagaria.  Bounded forcing axioms as principles of generic absoluteness , 2000, Arch. Math. Log..

[19]  Joel David Hamkins,et al.  The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $${\theta}$$θ-supercompact , 2013, Arch. Math. Log..

[20]  Joel David Hamkins.  Unfoldable Cardinals and The GCH , 2001, J. Symb. Log..

[21]  Joel David Hamkins.  A simple maximality principle , 2003, J. Symb. Log..

[22]  Joel David Hamkins,et al.  Superstrong and other large cardinals are never Laver indestructible , 2013, Arch. Math. Log..

[23]  Saharon Shelah.  Semiproper Forcing Axiom Implies Martin Maximum but Not PFA+ , 1987, J. Symb. Log..

[24]  Ernest Schimmerling,et al.  Hierarchies of forcing axioms I , 2008, J. Symb. Log..