Geodesic
A topological duality for the $F$-chains associated with the logic $C_\omega $
Mathematica Bohemica, Tome 142 (2017) no. 3, pp. 225-241

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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.
DOI : 10.21136/MB.2016.0079-14
Classification : 03B53, 03G10, 06D50
Keywords: paraconsistent logic; algebraic logic; dualities for ordered structures 
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Quiroga, Verónica; Fernández, Víctor. A topological duality for the $F$-chains associated with the logic $C_\omega $. Mathematica Bohemica, Tome 142 (2017) no. 3, pp. 225-241. doi: 10.21136/MB.2016.0079-14

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