Optimal strong Mal’cev conditions for omitting type 1 in locally finite varieties

We show that the class of locally finite varieties omitting type 1 has the following properties. This class is: definable by an idempotent, linear, strong Mal’cev condition in a language with one 4-ary function symbol; not definable by an idempotent, linear, strong Mal’cev condition in a language wi...

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Veröffentlicht in:Algebra universalis 2014-08, Vol.72 (1), p.91-100
Hauptverfasser: Kearnes, Keith, Marković, Petar, McKenzie, Ralph
Format: Artikel
Sprache:eng
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Zusammenfassung:We show that the class of locally finite varieties omitting type 1 has the following properties. This class is: definable by an idempotent, linear, strong Mal’cev condition in a language with one 4-ary function symbol; not definable by an idempotent, linear, strong Mal’cev condition in a language with only one function symbol of arity strictly less than 4; definable by an idempotent, linear, strong Mal’cev condition in a language with two 3-ary function symbols; not definable by an idempotent, linear, strong Mal’cev condition in a language with function symbols of arity less than 4 unless at least two of the symbols have arity 3.
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-014-0289-9