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A survey of Boolean algebras with operators. (English) Zbl 0811.06012

Rosenberg, Ivo (ed.) et al., Algebras and orders. Proceedings of the NATO Advanced Study Institute and Séminaire de mathématiques supérieures, Montréal, Canada, July 29 - August 9, 1991. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 389, 239-286 (1993).
The concept of a Boolean algebra with operators was invented and developed by Jónsson and Tarski. An operation \(f\) on a Boolean algebra is called an operator if it is additive in each of its arguments. An algebra \(A= (A_ 0,f_ i,i\in I)\) is called a Boolean algebra with operators. The paper, as indicated in its title, is a survey of results on Boolean algebras with operators which shows the unifying role of this concept in various branches of mathematics such as modal logic and modal algebras, closure algebras, monadic algebras, tense algebras, Boolean modules and dynamic algebras, algebras of programs as well as some other areas.
For the entire collection see [Zbl 0778.00036].

MSC:

06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
06-02 Research exposition (monographs, survey articles) pertaining to ordered structures
03G25 Other algebras related to logic
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
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