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math.LO2026
A counterexample to Kanalas' problem of continuously realising types
Morgan Rogers, Joshua Wrigley
We give an example of a coherent theory, a topological space, and a continuous assignment of the (model-theoretic) types of the theory to the points of the space, such that there i…
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.LO2025
On the theories classified by an étendue
Joshua Wrigley
We give a model-theoretic characterisation of the geometric theories classified by étendues -- the `locally localic' topoi. They are the theories where each model is determined, sy…