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 |
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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. |
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ISSN: | 0002-5240 1420-8911 |
DOI: | 10.1007/s00012-014-0289-9 |