Mathematica Bohemica, online first, 17 pp.

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

Verónica Quiroga, Victor Fernández

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

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:;

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 2010): 06D50, 03G10

DOI: 10.21136/MB.2016.0079-14

Full text available as PDF.

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