# [FOM] Strongly Minimal and Minimal Structures

Dave Marker marker at math.uic.edu
Sun Apr 18 23:06:53 EDT 2010

>1. Given a first order language L and its extension L', and an
>L'-structure M, if M as a L'-structure is strongly minimal, is it
>still strongly minimal as an L-structure?

Yes.   Any set definable in L is also definable in L' and hence
finite or cofinite.

>2. This is sort of related to the first one: By extending the
>language, can one always get a strongly minimal expansion for any
>minimal structure?

No. Consider (\omega, <).

>3. Is the conjecture that any minimal field is algebraically closed
>solved? (I know that F. Wagner proved it for the positive
>characteristic case)

This is still open.