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Théories d’algèbres de Boole munies d’idéaux distingués. I: Théorie élémentaires. (Theory of Boolean algebras equipped with distinguished ideals. I: Elementary theory). (French) Zbl 0659.03018
In 1949 Tarski classified the complete theories of Boolean algebras and proved that the isomorphism type of \({\mathbb{B}}\) is given by the lattice of definable ideals I and the number of atoms of \({\mathbb{B}}/_ I.\)
In this article it is shown that the same problem is solvable for Boolean algebras with an extra sequence of ideals. In this case the invariants are Heyting algebras of definable ideals with an additional unary operation * which allows to define something like the Cantor-Bendixson derivation.
Reviewer: K.Potthoff

MSC:
03C65 Models of other mathematical theories
03C05 Equational classes, universal algebra in model theory
06E05 Structure theory of Boolean algebras
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References:
[1] Comptes Rendus des Seances de l’Académie des Sciences. Série I: Mathématique 300 pp 125– (1985)
[2] Bulletin of the American Mathematical Society 55 pp 64– (1949)
[3] Algebra i Logika Seminar 3 pp 17– (1964)
[4] Comptes Rendus des Seances de l’Académie des Sciences. Série I: Mathématique 299 pp 415– (1984)
[5] Fundament a Mathematicae 47 pp 57– (1959)
[6] DOI: 10.2307/1969038 · Zbl 0060.06207
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