Please use this identifier to cite or link to this item: http://hdl.handle.net/10497/19501
Title: 
Authors: 
Issue Date: 
2018
Citation: 
Ho, W. K., Goubault-Larrecq, J., Jung, A., & Xi, X. (2018). The Ho-Zhao problem. Logical Methods in Computer Science, 14(1), 1-19. https://lmcs.episciences.org/4218
Abstract: 
Given a poset P, the set, Γ(P) of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory C of Posd (the category of posets and Scott-continuous maps) is said to be Γ-faithful if for any posets P and Q in C, Γ(P)≅Γ(Q) implies P≅Q. It is known that the category of all continuous dcpos and the category of bounded complete dcpos are Γ-faithful, while Posd is not. Ho & Zhao (2009) asked whether the category DCPO of dcpos is Γ-faithful. In this paper, we answer this question in the negative by exhibiting a counterexample. To achieve this, we introduce a new subcategory of dcpos which is Γ-faithful. This subcategory subsumes all currently known Γ-faithful subcategories. With this new concept in mind, we construct the desired counterexample which relies heavily on Johnstone's famous dcpo which is not sober in its Scott topology.
URI: 
ISSN: 
1860-5974 (online)
DOI: 
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