Zobrazeno 1 - 10
of 55
pro vyhledávání: '"Carai, Luca"'
Autor:
Bezhanishvili, Guram, Carai, Luca
Esakia's theorem states that Grzegorczyk's logic is the largest modal companion of intuitionistic propositional calculus. We prove that already the one-variable fragment of intuitionistic predicate calculus does not have the largest modal companion,
Externí odkaz:
http://arxiv.org/abs/2409.05607
Autor:
Carai, Luca, Moraschini, Tommaso
It is shown that the universal theory of the free pseudocomplemented distributive lattice is decidable and a recursive axiomatization is presented. This contrasts with the case of the full elementary theory of the finitely generated free algebras whi
Externí odkaz:
http://arxiv.org/abs/2409.03640
Autor:
Carai, Luca
G\"odel algebras are the Heyting algebras satisfying the axiom $(x \to y) \vee (y \to x)=1$. We utilize Priestley and Esakia dualities to dually describe free G\"odel algebras and coproducts of G\"odel algebras. In particular, we realize the Esakia s
Externí odkaz:
http://arxiv.org/abs/2406.05480
Autor:
Bezhanishvili, Guram, Carai, Luca
The Blok-Esakia Theorem establishes that the lattice of superintuitionistic logics is isomorphic to the lattice of extensions of Grzegorczyk's logic. We prove that the Blok-Esakia isomorphism $\sigma$ does not extend to the fragments of the correspon
Externí odkaz:
http://arxiv.org/abs/2405.09401
A quasivariety has the weak ES property when the epimorphisms between its finitely generated members are surjective. A characterization of quasivarieties with the weak ES property is obtained and a method for detecting failures of this property in qu
Externí odkaz:
http://arxiv.org/abs/2402.14745
The symmetric strict implication calculus $\mathsf{S^2IC}$, introduced in [5], is a modal calculus for compact Hausdorff spaces. This is established through de Vries duality, linking compact Hausdorff spaces with de Vries algebras-complete Boolean al
Externí odkaz:
http://arxiv.org/abs/2402.00528
Combining tools from category theory, model theory, and non-standard analysis we extend Baker-Beynon dualities to the classes of all Abelian $\ell$-groups and all Riesz spaces (also known as vector lattices). The extended dualities have a strong geom
Externí odkaz:
http://arxiv.org/abs/2310.13427
We generalize the classic Vietoris endofunctor to the category of compact Hausdorff spaces and closed relations. The lift of a closed relation is done by generalizing the construction of the Egli-Milner order. We describe the dual endofunctor on the
Externí odkaz:
http://arxiv.org/abs/2308.16823
We give an alternative, more geometric, proof of the well-known Joyal-Tierney Theorem in locale theory by utilizing Priestley duality for frames.
Externí odkaz:
http://arxiv.org/abs/2304.12651
We introduce the category of Heyting frames and show that it is equivalent to the category of Heyting algebras and dually equivalent to the category of Esakia spaces. This provides a frame-theoretic perspective on Esakia duality for Heyting algebras.
Externí odkaz:
http://arxiv.org/abs/2302.07913