Abstract
Let R 8 denote the 8-element bounded tower. G. Tardos has shown that C(R 8), the clone of all monotone functions on R 8, is not finitely generated. In this paper we show that the clone of all nonsurjective functions is finitely generated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. A. Baker and A. F. Pixley (1975) Polynomial interpolation and the Chinese remainder theorem for algebraic systems, Math. Z. 143, 165–174.
J. Demetrovics, L. Hannák, and L. Rónyai (1984) Near unanimity functions and partial orderings, Proc. 14. ISMVL, Manitoba, pp. 52–56.
D. Lau (1978) Bestimmung der Ordnung maximaler Klassen von Funktionen der k-wertigen Logik, Zeitschrift für Math. Logik und Grundlagen der Mathematik 24, 79–96.
I. G. Rosenberg (1980) Über die funktionale Vollstandigkeit in den mehrwertigen Logiken, Pozpr. CSAV Rada Math. Prir. Ved., Praha 80, 4, 3–93.
G. Tardos (1986) A not finitely generated maximal clone of monotone operations, Preprint of Math. Inst. of the Hungarian Acad. Sci (4), 1–10.
Author information
Authors and Affiliations
Additional information
Communicated by I. Rival
Rights and permissions
About this article
Cite this article
Demetrovics, J., Hannák, L. & Rónyai, L. On algebraic properties of monotone clones. Order 3, 219–225 (1986). https://doi.org/10.1007/BF00400285
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00400285