A Proof of Plotkin's Conjecture
In 1978, G. Plotkin [7] conjectured that for the three-element truthvalue dcpo T, if kappa > omega then the function space [T(kappa) -> T(kappa)] is not a retract of T(kappa). In this short paper, we constructively prove a stronger result that if kappa > omega then the function space [T(kappa) -> T(kappa)] is not a retract of the Cartesian product of any family of finite posets. Thus Plotkin's Conjecture is proved to be correct.
t(kappa) retract product coherent domain