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It is well-known that the theory of separably closed fields of some fixed positive characteristic and degree of imperfection is stable but not superstable. Also many $\omega$-stable expansions of fields are known ("coloured fields").

Is there an example of a non-$\omega$-stable superstable theory of (an expansion of) a field?

It is well-known that the theory of separably closed fields of some fixed positive characteristic and degree of imperfection is stable but not superstable. By a result of Cherlin and Shelah a superstable field is algebraically closed and many $\omega$-stable expansions of algebcaically fields are known ("coloured fields").

Is there an example of a non-$\omega$-stable superstable theory of (an expansion of) a field?

It is well-known that the theory of separably closed fields of some fixed positive characteristic and degree of imperfection is stable but not superstable.

Is there an example of a non-$\omega$-stable superstable theory of (an expansion of) a field?

It is well-known that the theory of separably closed fields of some fixed positive characteristic and degree of imperfection is stable but not superstable. Also many $\omega$-stable expansions of fields are known ("coloured fields").

Is there an example of a non-$\omega$-stable superstable theory of (an expansion of) a field?

It is well-known that the theory of separably closed fields of some fixed positive characteristic and degree of imperfection is stable but not superstable.

Is there an example of a non-$\omega$-stable superstable theory of a field?

It is well-known that the theory of separably closed fields of some fixed positive characteristic and degree of imperfection is stable but not superstable.

Is there an example of a non-$\omega$-stable superstable theory of (an expansion of) a field?