A Proof of Plotkin's Conjecture

Article type: Research Article

Authors: Yinbin, Lei | Maokang, Luo

Affiliations: 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

Note: [] Address for correspondence: School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, China

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.

Keywords: coherent domain, T[TeX:] ^{κ}, product, retract

DOI: 10.3233/FI-2009-0076

Journal: Fundamenta Informaticae, vol. 92, no. 3, pp. 301-306, 2009