15 citations · 43 across the 16 of their papers we have counts for
16 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…
Classifying toposes for non-geometric theories
Mark Kamsma
The classifying topos of a geometric theory is a topos such that geometric morphisms into it correspond to models of that theory. We study classifying toposes for different infinit…
Unstable independence from the categorical point of view
Mark Kamsma, Jiří Rosický
We give a category-theoretic construction of simple and NSOP-like independence relations in locally finitely presentable categories, and in the more general locally finitely mu…
Positive indiscernibles
Mark Kamsma
We generalise various theorems for finding indiscernible trees and arrays to positive logic: based on an existing modelling theorem for s-trees, we prove modelling theorems for str…
Dividing Lines between Positive Theories
Anna Dmitrieva, Francesco Gallinaro, Mark Kamsma
We give definitions of the properties OP, IP, -TP, TP, -TP, SOP, SOP and SOP in positive logic, and prove various implications and equivalences between th…
Independence relations for exponential fields
Vahagn Aslanyan, Robert Henderson, Mark Kamsma +1
We give four different independence relations on any exponential field. Each is a canonical independence relation on a suitable Abstract Elementary Class of exponential fields, sho…
Bilinear spaces over a fixed field are simple unstable
Mark Kamsma
We study the model theory of vector spaces with a bilinear form over a fixed field. For finite fields this can be, and has been, done in the classical framework of full first-order…
NSOP-like independence in AECats
Mark Kamsma
The classes stable, simple and NSOP in the stability hierarchy for first-order theories can be characterised by the existence of a certain independence relation. For each of th…
Kim-independence in positive logic
Jan Dobrowolski, Mark Kamsma
An important dividing line in the class of unstable theories is being NSOP, which is more general than being simple. In NSOP theories forking independence may not be as wel…
Type space functors and interpretations in positive logic
Mark Kamsma
We construct a 2-equivalence . Here is the 2-category of positive theories and $\mathfrak{Typ…
The Kim-Pillay theorem for Abstract Elementary Categories
Mark Kamsma
We introduce the framework of AECats (abstract elementary categories), generalising both the category of models of some first-order theory and the category of subsets of models. An…