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Some remarks on one-basedness. (English) Zbl 1073.03018

It is shown that in a simple theory a type analysable in one-based types is itself one-based. This improves previous results of Hrushovski and Chatzidakis, stating the same conclusion under strong assumptions (for instance in supersimple theories, and for stable stably embedded types). The proof follows E. Hrushovski’s approach in Proposition 3.4.1 of “The Manin-Mumford conjecture and the model theory of difference fields” [Ann. Pure Appl. Logic 112, 43–115 (2001; Zbl 0987.03036)]; anyhow, due to the larger – simple and possibly unstable – setting, it does not use germs of definable functions, and involves non-stationarity of types.

MSC:

03C45 Classification theory, stability, and related concepts in model theory

Citations:

Zbl 0987.03036
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References:

[1] Geometric stability theory (1996)
[2] Simple theories (2000)
[3] Classification theory, Proceedings, Chicago 1985 (1985)
[4] DOI: 10.1016/S0168-0072(01)00096-3 · Zbl 0987.03036
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