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On invariant classes of functions expressible by repetition-free definable formulas. (Russian) Zbl 1017.06005
The main results are as follows: (1) For each complete finite Boolean base $$B$$, the cardinality of the sets of invariant classes consisting of functions expressible by repetition-free formulas over $$B$$ is countable; (2) For each $$k>2$$, there exists a finite base $$B_k$$ of functions of $$k$$-valued logic such that the cardinality of the set of invariant classes consisting of the functions definable by repetition-free formulas over $$B_k$$ is $$2^\omega$$.
##### MSC:
 06E30 Boolean functions 03B50 Many-valued logic
##### Keywords:
Boolean function; repetition-free formula