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2019 Disjoint n-Amalgamation and Pseudofinite Countably Categorical Theories
Alex Kruckman
Notre Dame J. Formal Logic 60(1): 139-160 (2019). DOI: 10.1215/00294527-2018-0025

Abstract

Disjoint n-amalgamation is a condition on a complete first-order theory specifying that certain locally consistent families of types are also globally consistent. In this article, we show that if a countably categorical theory T admits an expansion with disjoint n-amalgamation for all n, then T is pseudofinite. All theories which admit an expansion with disjoint n-amalgamation for all n are simple, but the method can be extended, using filtrations of Fraïssé classes, to show that certain nonsimple theories are pseudofinite. As case studies, we examine two generic theories of equivalence relations, Tfeq and TCPZ, and show that both are pseudofinite. The theories Tfeq and TCPZ are not simple, but they have NSOP1. This is established here for TCPZ for the first time.

Citation

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Alex Kruckman. "Disjoint n-Amalgamation and Pseudofinite Countably Categorical Theories." Notre Dame J. Formal Logic 60 (1) 139 - 160, 2019. https://doi.org/10.1215/00294527-2018-0025

Information

Received: 13 October 2015; Accepted: 21 September 2016; Published: 2019
First available in Project Euclid: 29 January 2019

zbMATH: 07060311
MathSciNet: MR3911109
Digital Object Identifier: 10.1215/00294527-2018-0025

Subjects:
Primary: 03C13
Secondary: 03C45

Rights: Copyright © 2019 University of Notre Dame

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Vol.60 • No. 1 • 2019
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