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Article

Quiroga, Verónica ; Fernández, Víctor
A topological duality for the $F$-chains associated with the logic $C_\omega $. (English). Mathematica Bohemica, vol. 142 (2017), issue 3, pp. 225-241
MSC: 03B53, 03G10, 06D50 | MR 3695464 | Zbl 06770143 | DOI: 10.21136/MB.2016.0079-14
Keywords:
paraconsistent logic; algebraic logic; dualities for ordered structures
Summary:
In this paper we present a topological duality for a certain subclass of the $F_{\omega }$-structures defined by M. M. Fidel, which conform to a non-standard semantics for the paraconsistent N. C. A. da Costa logic $C_\omega $. Actually, the duality introduced here is focused on $F_\omega $-structures whose supports are chains. For our purposes, we characterize every \mbox {$F_\omega $-chain} by means of a new structure that we will call {\it down-covered chain} (DCC) here. This characterization will allow us to prove the dual equivalence between the category of $F_\omega $-chains and a new category, whose objects are certain special topological spaces (together with a distinguished family of open sets) and whose morphisms are particular continuous functions.
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