| Title:
|
Quasi-modal algebras (English) |
| Author:
|
Celani, Sergio |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
4 |
| Year:
|
2001 |
| Pages:
|
721-736 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Boolean algebras |
| Keyword:
|
modal algebras |
| Keyword:
|
Boolean spaces with relations |
| MSC:
|
03G05 |
| MSC:
|
06E25 |
| idZBL:
|
Zbl 0999.06012 |
| idMR:
|
MR1869464 |
| DOI:
|
10.21136/MB.2001.134115 |
| . |
| Date available:
|
2009-09-24T21:56:23Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134115 |
| . |
| Reference:
|
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| Reference:
|
[2] Bosangue M., Kwiatkowska M.: Re-interpreting the modal $\mu $-calculus. Modal Logic and Process Algebra: A Bisimulation Perspective.A. Ponse, M. de Rijke, Y. Venema (eds.), CSLI Lectures Notes, Stanford, CA, 1995. MR 1375698 |
| Reference:
|
[3] Goldblatt R.: Mathematics of Modality.CSLI Lectures Notes, Stanford, CA, 1993. Zbl 0942.03516, MR 1317099 |
| Reference:
|
[4] Goldblatt R.: 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. MR 1375698 |
| Reference:
|
[5] Jónsson B., Tarski A.: Boolean algebras with Operators, Part I.Amer. J. Math. 73 (1951), 891–939. MR 0044502, 10.2307/2372123 |
| Reference:
|
[6] Koppelberg S.: Topological duality.Handbook of Boolean Algebras, J. D. Monk, R. Bonnet (eds.) vol. 1, North-Holland, Amsterdam, 1989, pp. 95–126. MR 0991565 |
| Reference:
|
[7] Sambin G., Vaccaro V.: Topology and duality in modal logic.Ann. Pure Appl. Logic 37 (1988), 249–296. MR 0934369, 10.1016/0168-0072(88)90021-8 |
| . |
