Wagner, Frank O. Some remarks on one-basedness. (English) Zbl 1073.03018 J. Symb. Log. 69, No. 1, 34-38 (2004). 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. Reviewer: Carlo Toffalori (Camerino) Cited in 4 Documents MSC: 03C45 Classification theory, stability, and related concepts in model theory Keywords:one-based type; analysable type; simple theory Citations:Zbl 0987.03036 PDF BibTeX XML Cite \textit{F. O. Wagner}, J. Symb. Log. 69, No. 1, 34--38 (2004; Zbl 1073.03018) Full Text: DOI arXiv 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.