Monday, May 5, 20146:30 pmModels of PAGC 4214.03

# Submodel Lattices of Nerode Semirings

## Jim Schmerl

### University of Connecticut

Let TA be True Arithmetic, and let TA_2 be the set of Pi_2 sentences in TA.

If N is a model of TA_2, then the set Lt(N) of substructures of N that are also models of TA_2

forms a complete lattice. A Nerode semiring is a finitely generated model of TA_2.

I will be talking about some joint work with Volodya Shavrukov in which we investigate the possible lattices that are isomorphic to some Lt(N), where N is a Nerode semiring. Existentially closed models of TA_2 were studied long ago. The possible Lt(N) will also be considered for e.c. Nerode semirings.