Small clones and the projection property. (English) Zbl 1205.08002
The classification of minimal clones on finite universes into five types, due to the second author [in: L. Szabó et al. (eds.), Universal algebra, Colloq., Szeged/Hung. 1983, Colloq. Math. Soc. János Bolyai 43, 405–427 (1986; Zbl 0603.08005)], is extended to infinite universes and to multiclones: Every non-trivial clone contains a “small” clone of one of the five types. This result permits an alternate view of the projection property treated in a previous paper by the authors and M. G. Stone [Algebra Univers. 36, No. 2, 159–184 (1996; Zbl 0901.08001)].
Reviewer: Manfred Armbrust (Köln)
MSC:
| 08A40 | Operations and polynomials in algebraic structures, primal algebras |
| 08A62 | Finitary algebras |
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