A Proof of Plotkin's Conjecture

Authors:
Lei Yinbin;Luo Maokang
Affiliations:
(Correspd.) School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, China. lybhy@163.com;Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, China. makaluo@scu.edu.cn
Venue:
Fundamenta Informaticae
Year:
2009

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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.