25 citations · 61 across the 22 of their papers we have counts for
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A model category for modal logic
Luca Reggio
We define Quillen model structures on a family of presheaf toposes arising from tree unravellings of Kripke models, leading to a homotopy theory for modal logic. Modal preservation…
Arboreal Categories and Equi-resource Homomorphism Preservation Theorems
Samson Abramsky, Luca Reggio
The classical homomorphism preservation theorem, due to Łoś, Lyndon and Tarski, states that a first-order sentence is preserved under homomorphisms between structures if, and o…
Model completions for universal classes of algebras: necessary and sufficient conditions
George Metcalfe, Luca Reggio
Necessary and sufficient conditions are presented for the (first-order) theory of a universal class of algebraic structures (algebras) to admit a model completion, extending a char…
Beth definability and the Stone-Weierstrass Theorem
Luca Reggio
The Stone-Weierstrass Theorem for compact Hausdorff spaces is a basic result of functional analysis with far-reaching consequences. We introduce an equational logic asso…
An open mapping theorem for finitely copresented Esakia spaces
Samuel J. van Gool, Luca Reggio
We prove an open mapping theorem for the topological spaces dual to finitely presented Heyting algebras. This yields in particular a short, self-contained semantic proof of the uni…
Stone duality above dimension zero: Axiomatising the algebraic theory of C(X)
Vincenzo Marra, Luca Reggio
It has been known since the work of Duskin and Pelletier four decades ago that KH^op, the category opposite to compact Hausdorff spaces and continuous maps, is monadic over the cat…