On colimits and elementary embeddings

Journal of Symbolic Logic 78 (2):562-578 (2013)
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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 $\alpha$-strongly compact and $C^{(n)}$-extendible cardinals

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Maddy On The Multiverse.Claudio Ternullo - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Berlin: Springer Verlag. pp. 43-78.

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References found in this work

The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
[Omnibus Review].Akihiro Kanamori - 1981 - Journal of Symbolic Logic 46 (4):864-866.
Elementary Embeddings and Infinitary Combinatorics.Kenneth Kunen - 1971 - Journal of Symbolic Logic 36 (3):407-413.
C (N)-Cardinals.Joan Bagaria - 2012 - Archive for Mathematical Logic 51 (3-4):213-240.
Limites in Kategorien von Relationalsystemen.Michael Richter - 1971 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 17 (1):75-90.

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