Abstract
It is shown herein that on almost all closed Post classes only trivial congruences are possible. Closed Post classes having nontrivial congruences are indicated, and all congruences of these classes are described. For k≥3 closed classes having an infinity of congruences are indicated.
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Literature cited
A. I. Mal'tsev, “Iterative algebras and Post manifolds,” Algebra i Logika,5, No. 2, 5–24 (1966).
S. V. Yablonskii, V. B. Kudryavtsev, and G. P. Gavrilov, Functions of Logic Algebra and Post Classes [in Russian], Moscow (1966).
E. Post, Two-Valued Iterative Systems, London (1941).
Yu. I. Yanov and A. A. Muchnik, “On the existence of k-valued closed classes without a finite basis,” Dokl. Akad. Nauk SSSR,127, No. 1, 44–46 (1959).
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Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 725–734, May, 1973.
The author is grateful to S. V. Yablonskii for valuable comments and assistance in the research.
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Gorlov, V.V. On congruences in closed post classes. Mathematical Notes of the Academy of Sciences of the USSR 13, 434–438 (1973). https://doi.org/10.1007/BF01147474
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DOI: https://doi.org/10.1007/BF01147474