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2 results

  • PRINCIPAL AND SYNTACTIC CONGRUENCES IN CONGRUENCE-DISTRIBUTIVE AND CONGRUENCE-PERMUTABLE VARIETIES

  • Part of
  • BRIAN A. DAVEY, MARCEL JACKSON, MIKLÓS MARÓTI, RALPH N. MCKENZIE
  • Journal:
    Journal of the Australian Mathematical Society / Volume 85 / Issue 1 / August 2008
    Published online by Cambridge University Press:
    01 August 2008, pp. 59-74
    Print publication:
    August 2008
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  • We give a new proof that a finitely generated congruence-distributive variety has finitely determined syntactic congruences (or, equivalently, term finite principal congruences), and show that the same does not hold for finitely generated congruence-permutable varieties, even underthe additional assumption that the variety is residually very finite.

  • Minimal varieties and quasivarieties

  • Part of
  • Clifford Bergman, Ralph McKenzie
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 48 / Issue 1 / February 1990
    Published online by Cambridge University Press:
    09 April 2009, pp. 133-147
    Print publication:
    February 1990
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  • We prove that every locally finite, congruence modular, minimal variety is minimal as a quasivariety. We also construct all finite, strictly simple algebras generating a congruence distributive variety, such that the sett of unary term perations forms a group. Lastly, these results are applied to a problem in algebraic logic to give a sufficient condition for a deductive system to be structurally complete.