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CLASSIFICATION THEORY FOR ACCESSIBLE CATEGORIES

Published online by Cambridge University Press:  09 March 2016

M. LIEBERMAN  and
J. ROSICKÝ
M. LIEBERMAN
Affiliation:
DEPARTMENT OF MATHEMATICS AND STATISTICS MASARYK UNIVERSITY FACULTY OF SCIENCES KOTLÁŘSKÁ 2, 611 37 BRNO CZECH REPUBLICE-mail: lieberman@math.muni.cz
J. ROSICKÝ
Affiliation:
DEPARTMENT OF MATHEMATICS AND STATISTICS MASARYK UNIVERSITY FACULTY OF SCIENCES KOTLÁŘSKÁ 2, 611 37 BRNO CZECH REPUBLICE-mail: rosicky@math.muni.cz
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Abstract

We show that a number of results on abstract elementary classes (AECs) hold in accessible categories with concrete directed colimits. In particular, we prove a generalization of a recent result of Boney on tameness under a large cardinal assumption. We also show that such categories support a robust version of the Ehrenfeucht–Mostowski construction. This analysis has the added benefit of producing a purely language-free characterization of AECs, and highlights the precise role played by the coherence axiom.

Keywords

model theorycategorical logicabstract elementary classaccessible categoryGalois typestameness

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 1 , March 2016 , pp. 151 - 165
Copyright
Copyright © The Association for Symbolic Logic 2016 

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