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Simple Theories pp 147–186Cite as

Supersimple Theories

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Part of the book series: Mathematics and Its Applications ((MAIA,volume 503))

Abstract

Recall from Definition 2.8.12 that a simple theory is supersimple if for all finite tuples ā and all A there is a finite subset A 0 ⊆ A with \( { \downarrow _{A0}}A. \) The importance of supersimplicity stems from the fact that it allows a global, ordinal-valued rank, invariant under definable bijections, which orders definable sets and types and is compatible with independence. In fact, there are two (main) ranks; one suitable for complete types and one suitable for partial types. In this chapter, we shall again assume that we work in a simple theory (which need not be supersimple).

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Authors and Affiliations

  1. Institut Girard Desargues, Université Claude Bernard (Lyon-1), Villeurbanne, France

    Frank O. Wagner

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  1. Frank O. Wagner
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© 2000 Springer Science+Business Media Dordrecht

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Wagner, F.O. (2000). Supersimple Theories. In: Simple Theories. Mathematics and Its Applications, vol 503. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3002-0_5

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  • DOI: https://doi.org/10.1007/978-94-017-3002-0_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5417-3

  • Online ISBN: 978-94-017-3002-0

  • eBook Packages: Springer Book Archive

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