4 citations · 5 across the 10 of their papers we have counts for
7 papers · 1 filter
Vopěnka's Principle without Choice: Preservation under Symmetric Extensions
Tom de Groot, Wojciech Aleksander Wołoszyn
We give a detailed proof that every set-sized symmetric extension of a model of again satisfies , where is formulat…
Modal group theory: homomorphisms
Wojciech Aleksander Wołoszyn
I investigate modal group theory for arbitrary homomorphisms. Possibility is interpreted by the existence of a group homomorphism out of the given group, so the semantics is govern…
Modal group theory
Wojciech Aleksander Wołoszyn
I introduce modal group theory, in which we study the category of all groups, considering embeddability as providing a notion of modal possibility. Using HNN extensions and Britton…
The modal theory of linear orders
Wojciech Aleksander Wołoszyn
I study the modal theory of linear orders under embeddings, monotone maps, condensations, and end-extensions. I prove modality elimination for embeddings and monotone maps, show th…
The modal theory of the category of sets
Wojciech Aleksander Wołoszyn
We classify the propositional modal validities arising from the category of sets under its natural classes of morphisms. The resulting validities depend on the morphism class, the…
Grzegorczyk Logic Unlocked
Wojciech Aleksander Wołoszyn
The article offers a fresh perspective on Grzegorczyk logic Grz, introducing a simplified axiomatization and extending the analysis to its natural modal extensions, Grz.2 and Grz.3…
Modal model theory
Joel David Hamkins, Wojciech Aleksander Wołoszyn
We introduce the subject of modal model theory, where one studies a mathematical structure within a class of similar structures under an extension concept that gives rise to mathem…