Finitely many primitive positive clones. (English) Zbl 0656.08002
Let \(A\neq \emptyset\) be a finite set, \(O_ A\) denote the set of all n- ary operations on A, \(n\geq 1\). \(F\subseteq O_ A\) is said to be a primitive positive clone of \(f\in O_ A\) iff the graph of f is definable by a primitive positive formula (i.e. of the form \(\exists \forall atom)\). The authors prove that there are only finitely many primitive positive clones on A, and consequently there are only finitely many model companions for universal Horn classes generated by a finite algebra.
Reviewer: R.Franci
MSC:
| 08A40 | Operations and polynomials in algebraic structures, primal algebras |
| 03C05 | Equational classes, universal algebra in model theory |
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