Beta-models of ATR_0

by kamerynwilliams

This will be a talk for the CUNY MoPA seminar on Wednesday, November 29.

Recall that \mathsf{ATR}_0 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 (\omega,\mathcal{X}) 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 \mathsf{ATR}_0 is the omega-model whose sets are the hyperarithmetical sets.