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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.

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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