Exact saturation in simple and NIP theories

Itay Kaplan; Saharon Shelah; Pierre Simon

doi:10.1142/S0219061317500015

Exact saturation in simple and NIP theories

Itay Kaplan^*, Saharon Shelah, Pierre Simon

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

A theory T is said to have exact saturation at a singular cardinal ? if it has a ?-saturated model which is not ?+-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.

Original language	American English
Article number	1750001
Journal	Journal of Mathematical Logic
Volume	17
Issue number	1
DOIs	https://doi.org/10.1142/S0219061317500015
State	Published - 1 Jun 2017

Bibliographical note

Funding Information:
The first author would like to thank the Israel Science Foundation for partial support of this research (Grant No. 1533/14)

Publisher Copyright:
© 2017 World Scientific Publishing Company.

Keywords

NIP theories
Saturated models
classification theory
distal theories
simple theories

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10.1142/S0219061317500015

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Exact saturation in simple and NIP theories

Abstract

Bibliographical note

Keywords

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