[FOM] Strongly Minimal and Minimal Structures
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
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
This is still open.
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