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2 results

  • Fregean subtractive varieties with definable congruence

  • Part of
  • Paolo Agliano
  • Journal:
    Journal of the Australian Mathematical Society / Volume 71 / Issue 3 / December 2001
    Published online by Cambridge University Press:
    09 April 2009, pp. 353-366
    Print publication:
    December 2001
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  • In this paper we investigate subtractive varieties of algebras that are Fregean in order to get structure theorems about them. For instance it turns out that a subtractive variety is Fregean and has equationally definable principal congruences if and only if it is termwise equivalent to a variety of Hilbert algebras with compatible operations. Several examples are provided to illustrate the theory.

  • Congruence quasi-orderability in subtractive varieties

  • Part of
  • Paolo Agliano
  • Journal:
    Journal of the Australian Mathematical Society / Volume 71 / Issue 3 / December 2001
    Published online by Cambridge University Press:
    09 April 2009, pp. 421-446
    Print publication:
    December 2001
    • Article
      • You have access
    • PDF
    • Export citation

  • In this paper we investigate subtractive varieties of algebras that are congruence quasi-orderable. Though this concept has its origin in abstract algebraic logic, it seems to be worth investigating in a purely algebraic fashion. Besides clarifying the algebraic meaning of this notion, we obtain several structure theorems about such varieties. Also several examples are provided to illustrate the theory.