5 papers · 1 filter
Conceptual completeness for subgeometric logics
Ivan Di Liberti, Umberto Tarantino, Lingyuan Ye
We explore the notion of conceptual completeness for a fragment of geometric logic in the framework developed by the first and third author. Unlike its traditional interpretation a…
Duality theory for categorical theories
Lingyuan Ye
We have generalised the notion of categorical theory in model theory to the context of coherent theories. We prove a duality result between the full sub-2-category of pretopoi whic…
The Synthetic Sierpiński Cone
Fredrik Bakke, Jonathan Sterling, Mark Damuni Williams +1
In domains, categories, and toposes, the Sierpiński cone construction glues onto a space a universal closed point lying below all the other points. Although this is a lax colimit,…
Coexact completion of profinite Heyting algebras and uniform interpolation
Lingyuan Ye
This paper shows that the sheaf representation of finitely generated free Heyting algebras constructed by Ghilardi and Zawadowski can be factored as the profinite completion of Hey…
Craig Interpolation for Subgeometric Logics
Ivan Di Liberti, Lingyuan Ye
We show that a vast class of finitary fragments of geometric logic admit a form of Craig interpolation property. In doing so, we provide a new dictionary to import technology from…