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


  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.