6 papers
Cofibrant generation of pure monomorphisms
Michael Lieberman, Leonid Positselski, Jiri Rosicky +1
We show that pure monomorphisms are cofibrantly generated---generated from a set of morphisms by pushouts, transfinite composition, and retracts---in any locally finitely presentab…
Accessible categories, set theory, and model theory: an invitation
Sebastien Vasey
We give a self-contained introduction to accessible categories and how they shed light on both model- and set-theoretic questions. We survey for example recent developments on the…
Sizes and filtrations in accessible categories
Michael Lieberman, Jiří Rosický, Sebastien Vasey
Accessible categories admit a purely category-theoretic replacement for cardinality: the internal size. Generalizing results and methods from arXiv:1708.06782, we examine set-theor…
On categoricity in successive cardinals
Sebastien Vasey
We investigate, in ZFC, the behavior of abstract elementary classes (AECs) categorical in many successive small cardinals. We prove for example that a universal $\mathbb{L}_{ω_1, ω…
The categoricity spectrum of large abstract elementary classes
Sebastien Vasey
The categoricity spectrum of a class of structures is the collection of cardinals in which the class has a single model up to isomorphism. Assuming that cardinal exponentiation is…
Categoricity in multiuniversal classes
Nathanael Ackerman, Will Boney, Sebastien Vasey
The third author has shown that Shelah's eventual categoricity conjecture holds in universal classes: class of structures closed under isomorphisms, substructures, and unions of ch…