Exact saturation in simple and NIP theories

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Journal of Mathematical Logic 17 (1):1750001 (2017)
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Abstract

A theory [Formula: see text] is said to have exact saturation at a singular cardinal [Formula: see text] if it has a [Formula: see text]-saturated model which is not [Formula: see text]-saturated. We show, under some set-theoretic assumptions, that any simple theory has exact saturation. Also, an NIP theory has exact saturation if and only if it is not distal. This gives a new characterization of distality.

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10.1142/s0219061317500015

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Distal and non-distal NIP theories.Pierre Simon - 2013 - Annals of Pure and Applied Logic 164 (3):294-318.
Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
Witnessing Dp-Rank.Itay Kaplan & Pierre Simon - 2014 - Notre Dame Journal of Formal Logic 55 (3):419-429.

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