Criteria for exact saturation and singular compactness

2020/03/01 by Kaplan, Itay, Ramsey, Nicholas, Shelah, Saharon
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2003.00597

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.

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