TITLE: Is there minimally functionally complete set of 4 binary operators?
QUESTION [0 upvotes]: Wikipedia gives examples of minial sets for one, two or three elements and also mentions that there is no irreducible complete set with four elements of binary operators.
On the contrary, russian wikipedia states that there is minimal set for four elements but i didn't manage to find anyone. Can you help?

REPLY [1 votes]: Russian Wikipedia doesn't say binary. For binary functions, any non-monotonic function doesn't belong to at least two other Post sets, so there is indeed no irreducible complete set with four elements of binary operators.
Set $\{0,\, 1,\, xy,\, x \oplus y \oplus z\}$ is irreducible.
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