Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality
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Publication:404568
DOI10.1016/j.jalgebra.2014.06.031zbMath1300.06001arXiv1306.2839OpenAlexW2167210166MaRDI QIDQ404568
Vincenzo Marra, Mai Gehrke, Samuel J. van Gool
Publication date: 4 September 2014
Published in: Journal of Algebra (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1306.2839
Priestley dualityStone dualitydistributive latticeMV-algebracompact Hausdorff spacespectral spacelattice-ordered abelian groupétale decompositionsheaf representation
Lattices and duality (06D50) MV-algebras (06D35) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) Presheaves and sheaves in general topology (54B40)
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Priestley duality for MV-algebras and beyond ⋮ A representation theorem for integral rigs and its applications to residuated lattices. ⋮ Difference-restriction algebras of partial functions with operators: discrete duality and completion ⋮ Hopfian \(\ell\)-groups, MV-algebras and AF \({\mathrm{C}^{*}}\)-algebras ⋮ A set-theoretic proof of the representation of MV-algebras by sheaves ⋮ Topological duality and algebraic completions ⋮ Sheaves and duality ⋮ Orders on groups, and spectral spaces of lattice-groups ⋮ An extension of Stone duality to fuzzy topologies and MV-algebras ⋮ MV-algebras, infinite dimensional polyhedra, and natural dualities ⋮ Germinal theories in Łukasiewicz logic ⋮ A categorical duality for algebras of partial functions ⋮ Inflationary BL-algebras obtained from 2-dimensional general overlap functions ⋮ Sheaf representations and locality of Riesz spaces with order unit
Cites Work
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- The dual adjunction between MV-algebras and Tychonoff spaces
- Advanced Łukasiewicz calculus and MV-algebras
- Representation theory of MV-algebras
- A Sahlqvist theorem for distributive modal logic
- The Priestley duality for Wajsberg algebras
- Stone duality for Dedekind \(\sigma\)-complete \(\ell\)-groups with order-unit
- Canonical extensions of double quasioperator algebras: an algebraic perspective on duality for certain algebras with binary operations
- Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
- Reticulated rings
- Priestley duality and quotient lattices of many-valued algebras
- Sheaf representation and Chinese Remainder Theorems
- Groupes et anneaux reticules
- Prime spectra of lattice-ordered abelian groups
- A topological duality for some lattice ordered algebraic structures including \(\ell\)-groups
- Compact representations of BL-algebras
- Extending Stone duality to multisets and locally finite MV-algebras.
- Algebraic foundations of many-valued reasoning
- A simplified duality for implicative lattices and \(l\)-groups
- Duality, projectivity, and unification in Łukasiewicz logic and MV-algebras
- On Priestley spaces of lattice-ordered algebraic structures
- Sheaves of abelian \(l\)-groups
- The intimate relationship between the McNaughton and the Chinese remainder theorems for MV-algebras
- Duality for double quasioperator algebras via their canonical extensions
- Lattice-ordered Abelian groups and Schauder bases of unimodular fans, II
- RATIONAL POLYHEDRA AND PROJECTIVE LATTICE-ORDERED ABELIAN GROUPS WITH ORDER UNIT
- Semisimple Algebras of Infinite Valued Logic and Bold Fuzzy Set Theory
- Representations of MV-algebras by sheaves
- Stably compact spaces
- Stone duality for real-valued multisets
- A New Proof of the Completeness of the Lukasiewicz Axioms
- The Lebesgue state of a unital abelian lattice-ordered group, II
- Lattice-ordered Abelian groups and Schauder bases of unimodular fans
- Jaffard-Ohm correspondence and Hochster duality
- Invariant Measures in Free MV-Algebras
- Global subdirect products
- The Order Structure of Stone Spaces and the TD‐Separation Axiom
- Coproducts of De Morgan algebras
- Applications of Duality in the Theory of Finitely Generated Lattice-Ordered Abelian Groups
- The Chinese remainder theorem and sheaf representations
- Bounded distributive lattice expansions
- Canonical Extensions, Esakia Spaces, and Universal Models
- The Lebesgue state of a unital abelian lattice-ordered group
- Free Vector Lattices
- An isomorphism principle in general topology
- Prime Ideal Structure in Commutative Rings
- Representation of Distributive Lattices by means of ordered Stone Spaces
- Lattices of continuous functions
- Boolean Algebras with Operators
- Bounded lattice expansions
