Beta-models of ATR_0
This will be a talk for the CUNY MoPA seminar on Wednesday, November 29.
Recall that is the subsystem of second-order arithmetic axiomatized by (basic axioms plus) arithmetical comprehension plus arithmetical transfinite recursion. Also recall that a beta-model of arithmetic is a model of second-order arithmetic which is correct about which of its set relations are well-founded. I will present a theorem, due to Simpson, that the intersection of all beta-models of is the omega-model whose sets are the hyperarithmetical sets.