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Orthogonality of types in separably closed fields. (English) Zbl 0645.03029
Classification theory, Proc. U.S.-Israel Workshop on Model Theory in Math. Logic, Chicago/IL 1985, Lect. Notes Math. 1292, 78-88 (1987).
[For the entire collection see Zbl 0625.00010.]
Separably closed fields are the only known examples of stable but not superstable fields. After giving clear preliminary and background information the authors concentrate on 1-types: they construct families of mutually orthogonal types of rank 1 and then give a class of more complicated examples of conjugate types which serve to prove that various dimensional order properties, including DOP, hold, hence many somewhat saturated models exist. As mentioned by the authors, F. Delon had parallel and independent results in her paper: “Idéaux et types sur les corps séparablement clos, expository paper” [Mém. Soc. Math. France, Nouv. Sér. (to appear)] where she proved that separably closed fields have (only) stable pairs and have DOP, answering positively the question raised by Bouscaren (in contrast to her result for the superstable case) of whether one could have a stable theory with stable pairs and DOP.
Reviewer: Ch.Berline

03C60 Model-theoretic algebra
03C45 Classification theory, stability and related concepts in model theory
12L12 Model theory of fields