Dec

15

Tue

Title: Automorphism argument and reverse mathematics

by Keita Yokoyama (Japan Advanced Institute of Science and Technology) as part of Computability theory and applications

Abstract

In the study of models of Peano (or first-order) arithmetic, there are

many results on recursively saturated models and their automorphisms.

Here, we apply such an argument to models of second-order arithmetic

and see that any countable recursively saturated model (M,S) of WKL_0*

is isomorphic to its countable coded omega-submodel if

Sigma_1-induction fails in (M,S). From this result, we see some

interesting but weird properties of WKL_0* with the absence of

Sigma_1-induction such as the collapse of analytic hierarchy. This

argument can also be applied to the reverse mathematical study of

Ramsey’s theorem for pairs (RT22), and we see some new relations

between the computability-theoretic characterizations of RT22 and the

famous open question on the first-order part of RT22+RCA_0.

This work is a part of a larger project joint with Marta Fiori

Carones, Leszek Kolodziejczyk, Katarzyna Kowalik and Tin Lok Wong.

## University of Hawaiʻi at Mānoa