On the strength of admissible determinacy
by
Andres Caicedo
California Institute of Technology
Coauthors: Diego Rojas

For a real x let r_x=w₁^CK(x) be the first ordinal not recursive in x and let M_x=L_rx[x], so M_x is the smallest transitive model of KP that has x as an element. Originally considered by Andy Lewis, admissible determinacy is the statement that there is a real x such that M_x satisfies Ordinal Determinacy. We present some partial results towards determining the consistency strength of this hypothesis.

Date received: February 21, 2007