The set of maximal closed classes of operations on an infinite setA has cardinality $$2^{2^{^{\left| A \right|} } }$$
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[1] Some maximal closed classes of operations on infinite sets , 1974 .
[2] Emil L. Post. The two-valued iterative systems of mathematical logic , 1942 .
[3] Ivo G. Rosenberg. The Number of Maximal Closed Classes in the Set of Functions over a Finite Domain , 1973, J. Comb. Theory, Ser. A.