55 citations · 130 across the 18 of their papers we have counts for
21 papers
Topological Duality for Distributive Lattices: Theory and Applications
Mai Gehrke, Sam van Gool
This book is a course in Stone-Priestley duality theory, with applications to logic and theoretical computer science. Our target audience are graduate students and researchers in m…
Stone duality for spectral sheaves and the patch monad
Clemens Berger, Mai Gehrke
We establish a duality between global sheaves on spectral spaces and right distributive bands. This is a sheaf-theoretical extension of classical Stone duality between spectral spa…
Substitution Principle and semidirect products
Célia Borlido, Mai Gehrke
In the classical theory of regular languages the concept of recognition by profinite monoids is an important tool. Beyond regularity, Boolean spaces with internal monoids (BiMs) we…
Uniform Birkhoff
Mai Gehrke, Michael Pinsker
We show that pseudovarieties of finitely generated algebras, i.e., classes of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can…
A duality theoretic view on limits of finite structures: Extended version
Mai Gehrke, Tomáš Jakl, Luca Reggio
A systematic theory of structural limits for finite models has been developed by Nesetril and Ossona de Mendez. It is based on the insight that the collection of finite structures…
A Cook's tour of duality in logic: from quantifiers, through Vietoris, to measures
Mai Gehrke, Tomas Jakl, Luca Reggio
We identify and highlight certain landmark results in Samson Abramsky's work which we believe are fundamental to current developments and future trends. In particular, we focus on…
Priestley duality for MV-algebras and beyond
Wesley Fussner, Mai Gehrke, Sam van Gool +1
We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice b…
A duality theoretic view on limits of finite structures
Mai Gehrke, Tomáš Jakl, Luca Reggio
A systematic theory of structural limits for finite models has been developed by Nesetril and Ossona de Mendez. It is based on the insight that the collection of finite structures…
Sheaves and Duality
M. Gehrke, S. J. v. Gool
It has long been known in universal algebra that any distributive sublattice of congruences of an algebra which consists entirely of commuting congruences yields a sheaf representa…
Difference hierarchies and duality with an application to formal languages
Célia Borlido, Mai Gehrke, Andreas Krebs +1
The notion of a difference hierarchy, first introduced by Hausdorff, plays an important role in many areas of mathematics, logic and theoretical computer science such as descriptiv…
A note on powers of Boolean spaces with internal semigroups
Célia Borlido, Mai Gehrke
Boolean spaces with internal semigroups generalize profinite semigroups and are pertinent for the recognition of not-necessarily regular languages. Via recognition, the study of ex…
An interpolant in predicate Gödel logic
Matthias Baaz, Mai Gehrke, Sam van Gool
A logic satisfies the interpolation property provided that whenever a formula Δ is a consequence of another formula Γ, then this is witnessed by a formula Θ which only refers to th…
Quantifiers on languages and codensity monads
Mai Gehrke, Daniela Petrisan, Luca Reggio
This paper contributes to the techniques of topo-algebraic recognition for languages beyond the regular setting as they relate to logic on words. In particular, we provide a genera…
The Schützenberger product for syntactic spaces
Mai Gehrke, Daniela Petrisan, Luca Reggio
Starting from Boolean algebras of languages closed under quotients and using duality theoretic insights, we derive the notion of Boolean spaces with internal monoids as recognisers…
Distributive envelopes and topological duality for lattices via canonical extensions
Mai Gehrke, Sam Van Gool
We establish a topological duality for bounded lattices. The two main features of our duality are that it generalizes Stone duality for bounded distributive lattices, and that the…
Stone duality, topological algebra, and recognition
Mai Gehrke
Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A part…
Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality
Mai Gehrke, Samuel J. van Gool, Vincenzo Marra
We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an esse…
A non-commutative Priestley duality
Andrej Bauer, Karin Cvetko-Vah, Mai Gehrke +2
We prove that the category of left-handed strongly distributive skew lattices with zero and proper homomorphisms is dually equivalent to a category of sheaves over local Priestley…
Finitely generated free Heyting algebras via Birkhoff duality and coalgebra
Nick Bezhanishvili, Mai Gehrke
Algebras axiomatized entirely by rank 1 axioms are algebras for a functor and thus the free algebras can be obtained by a direct limit process. Dually, the final coalgebras can be…
A view of canonical extension
Mai Gehrke, Jacob Vosmaer
This is a short survey illustrating some of the essential aspects of the theory of canonical extensions. In addition some topological results about canonical extensions of lattices…
Canonical extension and canonicity via DCPO presentations
Mai Gehrke, Jacob Vosmaer
The canonical extension of a lattice is in an essential way a two-sided completion. Domain theory, on the contrary, is primarily concerned with one-sided completeness. In this pape…