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Preprint Number 942

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942. Alex Kruckman
Disjoint n-amalgamation and pseudofinite countably categorical theories

Submission date: 13 October 2015


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 paper, 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 non-simple theories are pseudofinite. As case studies, we examine two generic theories of equivalence relations, T*feq and TCPZ, and show that both are pseudofinite. The theories T*feq and TCPZ are not simple, but they are NSOP1. This is established here for TCPZ for the first time.

Mathematics Subject Classification: 03C13, 03C45

Keywords and phrases:

Full text arXiv 1510.03539: pdf, ps.

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