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The theory of boolean algebras with an additional binary operation

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Abstract

This paper deals with Boolean algebras supplied with an additional binary operation, calledB-algebras for short.

The aim of the paper is to generalize some theorems concerning topological Boolean algebras to more comprehensive classes ofB-algebras, to formulate fundamental properties ofB-algebras, and to find more important relationships of these algebras to other known algebras.

The paper consists of two parts. At the beginning of the first one, several subclasses ofB-algebras are distinguished, and then, their basic properties, connections between them as well as certain relationships with other algebras, are investigated. In particular, it is shown that the class of Boolean algebras together with an arbitrary unary operation is polynomially equivalent to the class ofB 1-algebras.

The second part of the paper is concerned with the theory of filters and congruences inB-algebras.

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References

  1. S. L. Bloom,On regular congruences Colloquium Mathematicum 29 (1974), pp. 25–29.

    Google Scholar 

  2. R. I. Goldblatt,Metamathematics of modal logics (Part I),Reports on Mathematical Logic 6 (1975), pp. 41–77.

    Google Scholar 

  3. G. Grätzer,Universal Algebra, New York 1968.

  4. P. Halmos,Algebraic Logic, New York 1962.

  5. E. V. Huntington,Postulates for assertion conjunction, negation and equality Proceedings of the American Academy of Art and Sciences 72 (1937), pp. 1–44.

    Google Scholar 

  6. J. D. Kagan,An axiomatization of the topological Boolean algebras Zeitschrift für mathematische Logik und Grundlagen der Mathematik 18 (1972), pp. 103–106.

    Google Scholar 

  7. J. D. Kagan andR. Quackenbush,Monadic algebras Reports on Mathematical Logic 7 (1976), pp. 53–62.

    Google Scholar 

  8. E. J. Lemmon,An extension algebra and the modal system T,Notre Dame Journal of Formal Logic 1 (1960), pp. 3–12.

    Google Scholar 

  9. J. McKinsey andA. Tarski,The algebra of topology Annals of Mathematics 45 (1944), pp. 141–191.

    Google Scholar 

  10. H. Rasiowa andR. Sikorski,The Mathematics of Metamathematics, Warsaw 1970.

  11. R. Sikorski,Boolean Algebras, Berlin-Göttingen-Heidelberg-New York 1964.

  12. J. Słomiński,On the determining of the form of congruences in abstract algebras with equationally definable constant elements Fundamenta Mathematicae 48 (1960), pp. 325–341.

    Google Scholar 

  13. R. Suszko,Abolition of the Fregean Axiom Lecture Notes in Mathematics 453 (1975), Springer-Verlag, pp. 169–239.

    Google Scholar 

  14. R. Suszko,Identity connective and modality Studia Logica 27 (1971), pp. 7–39.

    Google Scholar 

  15. R. Suszko,Equational logic and theories in sentential languages,Colloquium Mathematicum 29 (1974), pp. 19–23.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Pedagogical College, Siedlce, Poland

    Bronisław Tembrowski

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  1. Bronisław Tembrowski
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Tembrowski, B. The theory of boolean algebras with an additional binary operation. Stud Logica 42, 389–405 (1983). https://doi.org/10.1007/BF01371628

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  • DOI: https://doi.org/10.1007/BF01371628

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