[FOM] Strongly Minimal and Minimal Structures.

[Jizhan Hong]

Hello, there.

I am a student learning model theory. Just wondering if anyone has
quick answers to the following questions related to (strongly) minimal
structures:

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? I believe it's not, but I
just couldn't find an explicit counter-example.

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?

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

Any help is appreciated!
Thanks,
Jizhan Hong