On selected developments in the theory of natural dualities

zbMath1446.08011arXiv1912.12901MaRDI QIDQ5129681

Miroslav Haviar

Publication date: 22 October 2020

Full work available at URL: https://arxiv.org/abs/1912.12901

zbMATH Keywords

natural dualityentailmentendodualisabilityendoprimalityfull and strong dualities

Mathematics Subject Classification ID

Lattices and duality (06D50) Quasivarieties (08C15) Natural dualities for classes of algebras (08C20)

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• Full dualisability is independent of the generating algebra
• Using coloured ordered sets to study finite-level full dualities
• Natural extensions and profinite completions of algebras
• Multisorted dualisability: change of base
• Structural entailment
• Full but not strong dualities at the finite level: extending the realm
• Applications of Priestley duality in transferring optimal dualities
• The theory of topological commutative groups
• The Pontryagin duality of compact O-dimensional semilattices and its applications
• Endoprimal distributive lattices are endodualisable
• Natural dualities in partnership
• Endoprimal algebras
• Not every full duality is strong!
• Dualisability. Unary algebras and beyond
• Full does not imply strong, does it?
• THE LATTICE OF ALTER EGOS
• Transferral of entailment in duality theory: Dualisability
• Transferral of entailment in duality theory II: Strong dualisability
• Ordered Topological Spaces and the Representation of Distributive Lattices
• Transferring Optimal Dualities: Theory and Practice
• Optimal natural dualities. II: General theory
• The syntax and semantics of entailment in duality theory
• Representation of Distributive Lattices by means of ordered Stone Spaces
• The Theory of Representation for Boolean Algebras
• A criterion for a finite endoprimal algebra to be endodualisable
• Endodualisable and endoprimal finite double Stone algebras

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