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Special Sons, Morley Sequences

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

Abstract

Let M be a model of T and p a type over M. Let N be an elementary extension of M that realizes all types of S n (M) for all n. A son q of p over N is called special if for every formula \( f(x,\overrightarrow y ) \), if \( a \) and \( b \) are in N and have the same type over M, and if \( q \vDash f(x,\overrightarrow a ) \), then \( q \vDash f(x,\overrightarrow b ) \). In other words, the fact that \( q \vDash f(x,\overrightarrow a ) \) depends only on the type of \( a \) over M. We also call q M-special to say that it is a special son of its restriction to M; in this case, the function that sends a formula \( f(x,\overrightarrow y ) \) to the set of all types over M of tuples a of N such that \( q \vDash f(x,\overrightarrow a ) \) is called an infinitary definition of q over M.

Keywords

Ultrametric Space Stable Type Independence Property Infinite Subset Elementary Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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