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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
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