A Proof of Plotkin's Conjecture

Abstract

In 1978, G. Plotkin [7] conjectured that for the three-element truthvalue dcpo T, if κ > ω then the function space [T $^{κ}$ → T $^{κ}$ ] is not a retract of T $^{κ}$ . In this short paper, we constructively prove a stronger result that if κ > ω then the function space [T $^{κ}$ → T $^{κ}$ ] is not a retract of the Cartesian product of any family of finite posets. Thus Plotkin's Conjecture is proved to be correct.