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

Quiroga, Verónica, and Fernández, Víctor. "A topological duality for the $F$-chains associated with the logic $C_\omega $." Mathematica Bohemica 142.3 (2017): 225-241. <http://eudml.org/doc/294098>.

@article{Quiroga2017,
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.},
author = {Quiroga, Verónica, Fernández, Víctor},
journal = {Mathematica Bohemica},
keywords = {paraconsistent logic; algebraic logic; dualities for ordered structures},
language = {eng},
number = {3},
pages = {225-241},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A topological duality for the $F$-chains associated with the logic $C_\omega $},
url = {http://eudml.org/doc/294098},
volume = {142},
year = {2017},
}

TY - JOUR
AU - Quiroga, Verónica
AU - Fernández, Víctor
TI - A topological duality for the $F$-chains associated with the logic $C_\omega $
JO - Mathematica Bohemica
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 142
IS - 3
SP - 225
EP - 241
AB - 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.
LA - eng
KW - paraconsistent logic; algebraic logic; dualities for ordered structures
UR - http://eudml.org/doc/294098
ER -