The dual adjunction between MV-algebras and Tychonoff spaces

DOI10.1007/s11225-012-9377-zzbMath1252.06006OpenAlexW1991966428MaRDI QIDQ454391

Luca Spada, Vincenzo Marra

Publication date: 1 October 2012

Published in: Studia Logica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11225-012-9377-z

zbMATH Keywords

dualityMV-algebrascompact Hausdorff spacescategorical equivalenceŁukasiewicz logicpiecewise linear mapsadjunctionTychonoff cuberational polyhedra\({\mathbb{Z}}\)-mapsChang's completeness theoremHölder's theoremWóicicki's theorem

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) (54D15) MV-algebras (06D35)

Related Items (19)

Ordered group-valued probability, positive operators, and integral representations ⋮ Changing a Semantics: Opportunism or Courage? ⋮ Profinite completions and MacNeille completions of finitely presented MV-algebras ⋮ Are locally finite MV-algebras a variety? ⋮ Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality ⋮ Ideals of semisimple MV-algebras and convergence along set-theoretic filters ⋮ General affine adjunctions, Nullstellensätze, and dualities ⋮ Polyhedral MV-algebras ⋮ The Morita-equivalence between MV-algebras and lattice-ordered abelian groups with strong unit. ⋮ Some remarks on divisible polyhedral MV-algebras ⋮ MV-algebras, infinite dimensional polyhedra, and natural dualities ⋮ Germinal theories in Łukasiewicz logic ⋮ Algebraic geometry for \(\ell \)-groups ⋮ Duality theory and skeleta for semisimple MV-algebras ⋮ ALGEBRAIC GEOMETRY FOR MV-ALGEBRAS ⋮ Riesz-McNaughton functions and Riesz MV-algebras of nonlinear functions ⋮ The two-sorted algebraic theory of states, and the universal states of MV-algebras ⋮ Sheaf representations and locality of Riesz spaces with order unit ⋮ The spectrum problem for abelian \(\ell\)-groups and MV-algebras

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• The Lebesgue state of a unital abelian lattice-ordered group
• The Theory of Representation for Boolean Algebras

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