Quasi-modal algebras

Sergio A. Celani

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 4, page 721-736
  • ISSN: 0862-7959

Abstract

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In this paper we introduce the class of Boolean algebras with an operator between the algebra and the set of ideals of the algebra. This is a generalization of the Boolean algebras with operators. We prove that there exists a duality between these algebras and the Boolean spaces with a certain relation. We also give some applications of this duality.

How to cite

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Celani, Sergio A.. "Quasi-modal algebras." Mathematica Bohemica 126.4 (2001): 721-736. <http://eudml.org/doc/248870>.

@article{Celani2001,
abstract = {In this paper we introduce the class of Boolean algebras with an operator between the algebra and the set of ideals of the algebra. This is a generalization of the Boolean algebras with operators. We prove that there exists a duality between these algebras and the Boolean spaces with a certain relation. We also give some applications of this duality.},
author = {Celani, Sergio A.},
journal = {Mathematica Bohemica},
keywords = {Boolean algebras; modal algebras; Boolean spaces with relations; Boolean algebras; modal algebras; Boolean spaces with relations},
language = {eng},
number = {4},
pages = {721-736},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Quasi-modal algebras},
url = {http://eudml.org/doc/248870},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Celani, Sergio A.
TI - Quasi-modal algebras
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 4
SP - 721
EP - 736
AB - In this paper we introduce the class of Boolean algebras with an operator between the algebra and the set of ideals of the algebra. This is a generalization of the Boolean algebras with operators. We prove that there exists a duality between these algebras and the Boolean spaces with a certain relation. We also give some applications of this duality.
LA - eng
KW - Boolean algebras; modal algebras; Boolean spaces with relations; Boolean algebras; modal algebras; Boolean spaces with relations
UR - http://eudml.org/doc/248870
ER -

References

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  1. 10.1093/jigpal/7.2.153, Log. J. IGPL 7 (1999), 153–172. (1999) MR1682045DOI10.1093/jigpal/7.2.153
  2. Re-interpreting the modal μ -calculus. Modal Logic and Process Algebra: A Bisimulation Perspective, A. Ponse, M. de Rijke, Y. Venema (eds.), CSLI Lectures Notes, Stanford, CA, 1995. (1995) MR1375698
  3. Mathematics of Modality, CSLI Lectures Notes, Stanford, CA, 1993. (1993) Zbl0942.03516MR1317099
  4. Saturation and the Hennessy-Milner Property, Modal Logic and Process Algebra: A Bisimulation Perspective, A. Ponse, M. de Rijke, Y. Venema (eds.), CSLI Lectures Notes, Stanford, CA, 1995. (1995) MR1375698
  5. 10.2307/2372123, Amer. J. Math. 73 (1951), 891–939. (1951) MR0044502DOI10.2307/2372123
  6. Topological duality, Handbook of Boolean Algebras, J. D. Monk, R. Bonnet (eds.) vol. 1, North-Holland, Amsterdam, 1989, pp. 95–126. (1989) MR0991565
  7. 10.1016/0168-0072(88)90021-8, Ann. Pure Appl. Logic 37 (1988), 249–296. (1988) MR0934369DOI10.1016/0168-0072(88)90021-8

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