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Minimal quasivarieties of endographs. (English. Russian original) Zbl 0803.08006
Math. Notes 51, No. 6, 570-576 (1992); translation from Mat. Zametki 51, No. 6, 59-68 (1992).
Let \(\langle A; p,f\rangle\) be an algebraic system containing a binary predicate symbol \(p\) and a unary function symbol \(f\). An algebraic system \(\langle A; p,f\rangle\) is said to be an endograph if it satisfies the quasi-identity \((\forall x)(\forall y)(p(x,y)\to p(f(x),f(y)))\). The author proves that a set of minimal quasivarieties of endographs which has no independent basis of quasi-identities has the cardinality of the continuum.
MSC:
08C15 Quasivarieties
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