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Decision problems for classes of diagonalizable algebras

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Abstract

We make use of a Theorem of Burris-McKenzie to prove that the only decidable variety of diagonalizable algebras is that defined by ‘τ0=1’. Any variety containing an algebra in which τ0≠1 is hereditarily undecidable. Moreover, any variety of intuitionistic diagonalizable algebras is undecidable.

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References

  1. S. Burris, R. McKenzie, Decidability and Boolean representations, Memoirs of the American Mathematical Society, 32 (1981) Number 246.

  2. R. Freese, R. McKenzie, The commutator, an overview, preprint.

  3. A. Grzegorczyk, Undecidability of some topological theories, Fundamenta Mathematicae 38 (1951), pp. 137–152.

    Google Scholar 

  4. R. Magari, The diagonalizable algebras (The algebraization of theories representing Theor, II), Bollettino della Unione Matematica Italiana (4) 12 (Suppl. fasc. 3) (1975), pp. 117–125.

    Google Scholar 

  5. F. Montagna, Undecidability of the first order theory of diagonalizable algebras, Studia Logica, 39 (1980), pp. 347–354.

    Google Scholar 

  6. G. Sambin, An effective fixed point theorem for intuitionistic diagonalizable algebras, Studia Logica 35 (1976), pp. 345–361.

    Google Scholar 

  7. A. Ursini, Intuitionistic diagonalizable algebras, Algebra Universalis 9 (1979), pp. 229–237.

    Google Scholar 

  8. H. Werner, Discriminator Algebra, Studien zur Algebra und ihre Anwendungen, Band 6, Akademie Verlag, Berlin 1978.

    Google Scholar 

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Ursini, A. Decision problems for classes of diagonalizable algebras. Stud Logica 44, 87–89 (1985). https://doi.org/10.1007/BF00370812

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  • DOI: https://doi.org/10.1007/BF00370812

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