Strong Types

  • Bruno Poizat
Part of the Universitext book series (UTX)


Lemma 16.1. In a stable theory T, let p be a type in S 1 (A) and let M be a model of T containing A. Then for every formula \( f(x,\overrightarrow y ) \) there is an equivalence relation \( E_f (\overrightarrow y ,\overrightarrow z ) \), with finitely many classes, defined by a formula with parameters in A, such that two tuples \( \overrightarrow a {\text{ and }}\overrightarrow b \) in M are congruent modulo E f if and only if all nonforking sons of p satisfy \( f(x,\overrightarrow a ) \leftrightarrow f(x,\overrightarrow b ) \).


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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Bruno Poizat
    • 1
  1. 1.Département des MathématiquesUniversite Claude Bernard Lyon IVilleurbanne CedexFrance

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