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Interpretability of the Cantor varieties. (English. Russian original) Zbl 0849.08007
Algebra Logic 34, No. 4, 258-262 (1995); translation from Algebra Logika 34, No. 4, 464-471 (1995).
A Cantor variety \(C_n\), \(n \geq 2\), is a variety of algebras with one \(n\)-ary functional symbol \(g\) and \(n\) unary functional symbols \(f_1, \dots, f_n\) satisfying the following identities: \(f_i(g(x_1,\dots, x_n)) = x_i\), \(1 \leq i \leq n\), \(g(f_1(x),\dots,f_n(x)) = x\).
An SC-theory (or a Mal’tsev theory) of a variety \(V\) is the collection of all strong Mal’tsev conditions satisfied in \(V\).
Theorem I. The SC-theory of the Cantor variety \(C_2\) has bases of any finite length \(\geq 1\).
Theorem II. The dimension of every Cantor variety \(C_n\) is infinite.
Reviewer: J.Duda (Brno)
MSC:
08B05 Equational logic, Mal’tsev conditions
03C05 Equational classes, universal algebra in model theory
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References:
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