Finitely determined arithmetical varieties need not be universally- finite. (English) Zbl 0604.08002
A variety V is finitely determined if it is generated by its finite members; it is arithmetical if it is both congruence permutable and congruence distributive; it is universally-finite if every universal sentence true in the class of its finite members is true in V. The result formulated in the title is proved.
Reviewer: J.Ježek
MSC:
| 08B10 | Congruence modularity, congruence distributivity |
| 08C10 | Axiomatic model classes |
| 03C60 | Model-theoretic algebra |
Keywords:
arithmetical variety; congruence permutable; congruence distributive; universally-finite; universal sentence; finite membersReferences:
| [1] | B. Jonsson,Algebras whose congruence lattices are distributive, Math. Scand.21 (1967), 110-121. · Zbl 0167.28401 |
| [2] | S. Tulipani,On the universal theory of classes of finite models, Trans. Amer. Math. Soc.284 (1984), 163-170. · Zbl 0521.03021 · doi:10.1090/S0002-9947-1984-0742418-9 |
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