The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras.
@article{bwmeta1.element.doi-10_1515_math-2016-0086,
author = {Jun Tao Wang and Xiao Long Xin and Arsham Borumand Saeid},
title = {Very true operators on MTL-algebras},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {955-969},
zbl = {1353.03082},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0086}
}
Jun Tao Wang; Xiao Long Xin; Arsham Borumand Saeid. Very true operators on MTL-algebras. Open Mathematics, Tome 14 (2016) pp. 955-969. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0086/