April 27
Dave Marker, University of Illinois at Chicago
Real closures of $\omega_1$-like models of PA

D'Aquino, Knight and Starchenko showed the real closure of a model of Peano Arithmetic is recursively saturated. Thus any two countable models of PA with the same standard system have isomorphic real closures. Charlie Steinhorn, Jim Schmerl and I showed that even for $\omega_1$-like model of PA the situation is very different. We construct $2^{\aleph_1}$ recursively saturated elementarily equivalent $\omega_1$-like models of PA with the same standard system and non-isomorphic real closures.

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