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On Colimits and Elementary Embeddings

Published online by Cambridge University Press:  12 March 2014

Joan Bagaria  and
Andrew Brooke-Taylor
Joan Bagaria
Affiliation:
Icrea (Institució Catalana de Recerca i Estudis Avancats), Departament de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona, Montalegre 6, 08001 Barcelona, Catalonia, Spain, E-mail:joan.bagaria@icrea.cat
Andrew Brooke-Taylor
Affiliation:
Group of Logic, Statistics & Informatics, Graduate School of System Informatics, Kobe University, Rokko-Dai 1-1, Nada, Kobe, 657-0013, Japan, E-mail:andrewbt@gmail.com
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Abstract

We give a sharper version of a theorem of Rosický, Trnková and Adámek [13], and a new proof of a theorem of Rosický [12], both about colimits in categories of structures. Unlike the original proofs, which use category-theoretic methods, we use set-theoretic arguments involving elementary embeddings given by large cardinals such as α-strongly compact and C(n)-extendible cardinals.

Keywords

Colimitselementary embeddingsVopěnka's Principlestrongly compact cardinalsaccessible categories
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 2 , June 2013 , pp. 562 - 578
Copyright
Copyright © Association for Symbolic Logic 2013

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References

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