Mathematica Bohemica, Vol. 142, No. 3, pp. 225-241, 2017


A topological duality for the $F$-chains associated with the logic $C_\omega$

Verónica Quiroga, Víctor Fernández

Received December 19, 2014.  First published December 19, 2016.

Abstract:  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 $F_\omega$-chain by means of a new structure that we will call 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.
Keywords:  paraconsistent logic; algebraic logic; dualities for ordered structures
Classification MSC:  06D50, 03G10
DOI:  10.21136/MB.2016.0079-14


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Affiliations:   Verónica Quiroga, Víctor Fernández, Basic Sciences Institute, National University of San Juan, Av. José Ignacio de la Roza Oeste 230, San Juan 5400, Argentina, e-mail: veronicaandreaquiroga@gmail.com; vlfernan@ffha.unsj.edu.ar

 
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