Geometrical Dualities for Łukasiewicz Logic

Luca Spada

Bollettino dell'Unione Matematica Italiana (2013)

  • Volume: 6, Issue: 3, page 749-763
  • ISSN: 0392-4041

Abstract

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This article develops a general dual adjunction between MV-algebras (the algebraic equivalents of Łukasiewicz logic) and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MV-algebras. Such a dual adjunction restricts to a duality between semisimple MV-algebras and closed subspaces of Tychonoff cubes. Further the duality theorem for finitely presented objects is obtained from the general adjunction by a further specialisation. The treatment is aimed at emphasising the generality of the framework considered here in the prototypical case of MV-algebras.

How to cite

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Spada, Luca. "Geometrical Dualities for Łukasiewicz Logic." Bollettino dell'Unione Matematica Italiana 6.3 (2013): 749-763. <http://eudml.org/doc/294035>.

@article{Spada2013,
abstract = {This article develops a general dual adjunction between MV-algebras (the algebraic equivalents of Łukasiewicz logic) and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MV-algebras. Such a dual adjunction restricts to a duality between semisimple MV-algebras and closed subspaces of Tychonoff cubes. Further the duality theorem for finitely presented objects is obtained from the general adjunction by a further specialisation. The treatment is aimed at emphasising the generality of the framework considered here in the prototypical case of MV-algebras.},
author = {Spada, Luca},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {749-763},
publisher = {Unione Matematica Italiana},
title = {Geometrical Dualities for Łukasiewicz Logic},
url = {http://eudml.org/doc/294035},
volume = {6},
year = {2013},
}

TY - JOUR
AU - Spada, Luca
TI - Geometrical Dualities for Łukasiewicz Logic
JO - Bollettino dell'Unione Matematica Italiana
DA - 2013/10//
PB - Unione Matematica Italiana
VL - 6
IS - 3
SP - 749
EP - 763
AB - This article develops a general dual adjunction between MV-algebras (the algebraic equivalents of Łukasiewicz logic) and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MV-algebras. Such a dual adjunction restricts to a duality between semisimple MV-algebras and closed subspaces of Tychonoff cubes. Further the duality theorem for finitely presented objects is obtained from the general adjunction by a further specialisation. The treatment is aimed at emphasising the generality of the framework considered here in the prototypical case of MV-algebras.
LA - eng
UR - http://eudml.org/doc/294035
ER -

References

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