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Apr 22, 2019 at 18:25 comment added Alex Kruckman Off the top of my head, I don't know any "natural" examples other than the ones on the page I linked to in my first comment: $\mathbb{Q}$ACFA and imperfect bounded PAC fields.
Apr 22, 2019 at 18:19 comment added huurd Oh sorry I meant "simple, non supersimple, non stable" of course... do you have any reference talking about "natural" ones (coming from algebra or other branches of mathematics) ?
Apr 22, 2019 at 18:15 comment added Alex Kruckman A good reference for examples in model theory is forkinganddividing.com. Note that simple non-supersimple includes stable non-superstable, and there are many such examples. "Natural" strictly simple examples are harder to come by, but you can cook up lots of examples by combining supersimple theories with strictly stable theories in various ways.
Apr 22, 2019 at 18:07 comment added huurd By the way, what are the known examples of simple non-supersimple theories ?
Apr 22, 2019 at 17:06 history answered Alex Kruckman CC BY-SA 4.0