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.
Un chant mystérieux tombe des astres d’or
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© 2000 Springer Science+Business Media New York
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Poizat, B. (2000). Special Sons, Morley Sequences. In: A Course in Model Theory. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8622-1_12
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DOI: https://doi.org/10.1007/978-1-4419-8622-1_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6446-0
Online ISBN: 978-1-4419-8622-1
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