Annals of Pure and Applied Logic 172 (9):102992 (2021)

Authors
Nicholas Ramsey
University of California, Los Angeles
Abstract
We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satisfying certain set-theoretic hypotheses. We also give criteria for a theory to have singular compactness.
Keywords Model theory  Classification theory  Exact saturation  Singular compactness
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DOI 10.1016/j.apal.2021.102992
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References found in this work BETA

Theories Without the Tree Property of the Second Kind.Artem Chernikov - 2014 - Annals of Pure and Applied Logic 165 (2):695-723.
On Model-Theoretic Tree Properties.Artem Chernikov & Nicholas Ramsey - 2016 - Journal of Mathematical Logic 16 (2):1650009.
Toward Classifying Unstable Theories.Saharon Shelah - 1996 - Annals of Pure and Applied Logic 80 (3):229-255.
On ◁∗-Maximality.Mirna Džamonja & Saharon Shelah - 2004 - Annals of Pure and Applied Logic 125 (1-3):119-158.
Exact Saturation in Simple and NIP Theories.Itay Kaplan, Saharon Shelah & Pierre Simon - 2017 - Journal of Mathematical Logic 17 (1):1750001.

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