3 papers
math.LO2025
Existential completions and Herbrand's theorem
Joshua L. Wrigley
Recently, Abbadini and Guffanti gave an algebraic proof of Herbrand's theorem using a completion for Lawvere doctrines that freely adds existential and universal quantifiers. A mor…
math.CT2024
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…
math.CT2023
The Geometric Completion of a Doctrine
Joshua Wrigley
As several different formal systems with inequivalent syntax may describe equivalent semantics, it is possible to find `completions' to more expressive syntaxes that are semantical…