Profinite relational structures

• Author(s): Janelidze, George ; Sobral, Manuela
• Date: 2008
• Persistent ID: http://hdl.handle.net/10316/11239
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Ordered (preordered) topological spaces; Priestley space; Stone space; Fibration; Topological functor; Profinite; Relational structure; Quasi-variety
• Document Type: Preprint
• Language: English

Description

We show that a topological preorder (on a Stone space) is profinite if and only if it is inter-clopen, i.e. it can be presented as an intersection of closed-andopen preorders on the same space. In particular this provides a new characterization of the so-called Priestley spaces. We then extend this from preorders to general relational structures satisfying some conditions. We also give a stronger condition that has a rather clear model-theoretic meaning. South African NRF; FCT/Centro de Matemática da Universidade de Coimbra