  Let us now return to our overview of large cardinal axioms.  After strongly inaccessible cardinals there are Mahlo cardinals, indescribable cardinals, and ineffable cardinals.  All of these large cardinal axioms can be derived in a uniform way using the traditional variety of reflection principles (see Tait 2005) but there are limitations on how far this variety of reflection principles can take one.  For under a very general characterization of such principles it is known that they cannot yield the Erdős cardinal κ(ω).  See Koellner (2009).