a1 Department of Mathematics, La Trobe University, Victoria, Australia (email: email@example.com)
a2 Department of Mathematics, La Trobe University, Victoria, Australia (email: firstname.lastname@example.org)
a3 János Bolyai Mathematical Institute, University of Szeged, Szeged, Hungary (email: email@example.com)
a4 Department of Mathematics, Vanderbilt University, Nashville, TN, USA (email: firstname.lastname@example.org)
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 under the additional assumption that the variety is residually very finite.
(Received August 30 2006)
(Accepted February 23 2007)
2000 Mathematics subject classification
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The second author was supported by ARC Discovery Project Grant DP0342459. The third author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA), grant nos. T 37877 and T 48809.