Exact saturation in simple and NIP theories

Itay Kaplan; Saharon Shelah; Pierre Simon

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arXiv · 1510.02741

Exact saturation in simple and NIP theories

Itay Kaplan·Saharon Shelah·Pierre Simon

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Abstract

A theory $T$ is said to have exact saturation at a singular cardinal $\kappa$ if it has a $\kappa$-saturated model which is not $\kappa^{+}$-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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BibTeX RIS

Itay Kaplan, Saharon Shelah, Pierre Simon. 2015-10-09. Exact saturation in simple and NIP theories. https://arxiv.org/abs/1510.02741

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