 The issue, of course, is whether one can have an “L-like” model (one that yields an “effectively complete” axiom) at this level. There is reason to believe that one can. There is now a candidate model LΩ that yields an axiom V = LΩ with the following features: First, V = LΩ is “effectively complete.” Second, V = LΩ is compatible with all large cardinal axioms. Thus, on this scenario, the ultimate theory would be the (open-ended) theory ZFC + V = LΩ + LCA, where LCA is a schema standing for “large cardinal axioms.” The large cardinal axioms will catch instances of Gödelian independence and the axiom V = LΩ will capture the remaining instances of independence. This theory would imply CH and settle the remaining undecided statements. Independence would cease to be an issue. 