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

Voir la notice de l'article dans Czech Digital Mathematics Library

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
Mots-clés : paraconsistent logic; algebraic logic; dualities for ordered structures 
@article{10_21136_MB_2016_0079_14,
     author = {Quiroga, Ver\'onica and Fern\'andez, V{\'\i}ctor},
     title = {A topological duality for the $F$-chains associated with the logic $C_\omega $},
     journal = {Mathematica Bohemica},
     pages = {225--241},
     publisher = {mathdoc},
     volume = {142},
     number = {3},
     year = {2017},
     doi = {10.21136/MB.2016.0079-14},
     mrnumber = {3695464},
     zbl = {06770143},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2016.0079-14/}
}
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
SP  - 225
EP  - 241
VL  - 142
IS  - 3
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2016.0079-14/
DO  - 10.21136/MB.2016.0079-14
LA  - en
ID  - 10_21136_MB_2016_0079_14
ER  - 
%0 Journal Article
%A Quiroga, Verónica
%A Fernández, Víctor
%T A topological duality for the $F$-chains associated with the logic $C_\omega $
%J Mathematica Bohemica
%D 2017
%P 225-241
%V 142
%N 3
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2016.0079-14/
%R 10.21136/MB.2016.0079-14
%G en
%F 10_21136_MB_2016_0079_14
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. https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2016.0079-14/

Cité par Sources :