Series: Penn State Logic Seminar Date: Tuesday, September 14, 2004 Time: 2:30 - 3:45 PM Place: 307 Boucke Building Speaker: Stephen G. Simpson, Penn State, Mathematics Title: A Symmetric beta-Model Abstract: A beta-model is a nonempty subset of the reals which is an elementary submodel of the reals with respect to Sigma^1_1 formulas. It is known that any beta-model properly includes the set of hyperarithmetical reals. We show that there exists a countable beta-model M such that, for all reals X and Y in M, X is definable from Y over M if and only if X is hyperarithmetical relative to Y. The proof uses a factorization lemma for a variant of Gandy-Harrington forcing.