LARGE ORDINALS

Let j be an elementary embedding of V-lambda into V-lambda that is not the identity, and let kappa be the critical point of j. Let A be the closure of {j} under the operation a(b) of application, and let Omega be the closure of {kappa} under the operation min {xi: a(xi) greater t han or equal to b(a)}. We give a complete description of the set Omega under an assumption (Threshold Hypothesis) on cyclic left distributiv e algebras. (C) 1997 Academic Press.