# Dividing and conquering: locally definable sets as stand-alone structures

## Alice Medvedev

### City College -- CUNY

In what sense is the ring of polynomials in one variable over a field k interpretable in k? In what sense is the subgroup of G generated by a definable subset D of G interpretable in G? These questions have been answered in various particular contexts by various people. We set up a general formalism to treat such piece-wise interpreted objects as stand-alone multi-sorted first-order structures. This formalism is motivated by our quest to create a model-theoretically tractable analog of sheaf theory. This is a very preliminary report on joint work with Ramin Takloo-Bighash.

Prof. Medvedev is a model theorist, teaching at City College in the CUNY system. She received her doctorate from the University of California-Berkeley, under the supervision of Tom Scanlon, and subsequently held postdoctoral positions at Berkeley and at the University of Illinois-Chicago.