FPM 1996, vol. 2, no. 1, pp. 161-170

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1996, VOLUME 2, NUMBER 1, PAGES 161-170

On properties of maximal homomorphic prototypes of $k$ -valued logic in $l$ -valued logic

A. V. Makarov

Abstract

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The properties of the set $$
{\cal L}_{k}^{l} $$ of all closed subsets of $l$ -valued logic $P$ _l, which may be reflected homomorphically onto $P$ _k are investigated. We determined all maximal elements of $$ {\cal L}_{k}^{l} $$ and proved that any maximal element is generated by a single function. The asymptotic formula for the number of in pairs nonisomorphic maximal elements of $$ \bigcup
_{k=2}^l {\cal L}_{k}^{l} $$ was obtained.

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On properties of maximal homomorphic prototypes of k-valued logic in l-valued logic

On properties of maximal homomorphic prototypes of $k$ -valued logic in $l$ -valued logic