Admissible Suslin cardinals in L(R)

Abstract

AbstractAssuming AD + (V = L(R)), it is shown that for κ an admissible Suslin cardinal, o(κ) (= the order type of the stationary subsets of κ) is “essentially” regular and closed under ultrapowers in a manner to be made precise. In particular, o(κ) ≫ κ+, κ++, etc. It is conjectured that this characterizes admissibility for L(R).