MathDB

Let P be a finite, partially ordered set with one largest element, which is the only upper bound of the set of minimal elements. Prove that any monotonic function

f : P^n\to P

can be written in the form

g( x_1 , x_2 , ..., x_n , c_1 , ..., c_m )

, where

c_i\in P

and g is a monotonic, idempotent function. (g is idempotent iff

g(x , x , ..., x) = x\,\forall x\in P

)

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