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Jul 9, 2012 at 8:42 comment added Dima Sustretov "A superstable non-ω-stable expansion of a field" would be a more precise term. I have updated the question.
Jul 8, 2012 at 21:54 comment added Goldstern I may have misunderstood your question. I meant fields in the language of rings.
Jul 8, 2012 at 20:56 comment added Dima Sustretov Dear Goldstern, I am unsure what you mean by this statement. Surely there are known stable theories of fields that do not fit the list in the sense that their structure is not of a pure algebraically or separably closed field, e.g. the "bad field" of Baudisch-Martin-Pizarro-Hils-Wagner and all kinds of fields with "coloured points" constructed by Poizat.
Jul 8, 2012 at 16:18 history answered Goldstern CC BY-SA 3.0