8 papers
Cellular generation revisited
Sean Cox, Mark Kamsma, Jiří Rosický
Cellular generation, which generalises cofibrant generation, is an important categorical smallness condition on a class of morphisms. A general challenge is to determine whether a…
Positive Logic: An Introduction for Model Theorists
Mark Kamsma
Positive logic is a generalisation of full first-order logic that does not have negation built in. Still, many model-theoretic ideas, tools and techniques work perfectly fine in po…
Cofibrant generation of pure monomorphisms in presheaf categories
Sean Cox, Jonathan Feigert, Mark Kamsma +2
We characterise when the pure monomorphisms in a presheaf category are cofibrantly generated in terms of the category . In particular, when…
Lifting independence along functors
Mark Kamsma, Jiří Rosický
Given a functor and a model-theoretic independence relation on , we can lift that independence relation along to by…
Existentially closed models and locally zero-dimensional toposes
Mark Kamsma, Joshua Wrigley
The notion of an existentially closed model is generalised to a property of geometric morphisms between toposes. We show that important properties of existentially closed models ex…
Corrigendum to "Kim-independence in positive logic"
Jan Dobrowolski, Mark Kamsma
The proof of the Independence Theorem for Kim-independence in positive thick NSOP theories from (Dobrowolski and Kamsma, 2022) contains a gap. The theorem is still true, and in…