Criteria for exact saturation and singular compactness

Itay Kaplan; Nicholas Ramsey; Saharon Shelah

doi:10.1016/j.apal.2021.102992

Criteria for exact saturation and singular compactness

Itay Kaplan, Nicholas Ramsey, Saharon Shelah

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

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.

Original language	English
Article number	102992
Journal	Annals of Pure and Applied Logic
Volume	172
Issue number	9
DOIs	https://doi.org/10.1016/j.apal.2021.102992
State	Published - 1 Oct 2021

Keywords

Classification theory
Exact saturation
Model theory
Singular compactness

All Science Journal Classification (ASJC) codes

Logic

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10.1016/j.apal.2021.102992

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title = "Criteria for exact saturation and singular compactness",

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 = "Classification theory, Exact saturation, Model theory, Singular compactness",

author = "Itay Kaplan and Nicholas Ramsey and Saharon Shelah",

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year = "2021",

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AU - Ramsey, Nicholas

AU - Shelah, Saharon

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AB - 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.

KW - Classification theory

KW - Exact saturation

KW - Model theory

KW - Singular compactness

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DO - 10.1016/j.apal.2021.102992

M3 - مقالة

SN - 0168-0072

VL - 172

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 9

M1 - 102992

ER -

Criteria for exact saturation and singular compactness

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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