Very true operators on MTL-algebras

Jun Tao Wang, Xiao Long Xin, and Arsham Borumand Saeid. "Very true operators on MTL-algebras." Open Mathematics 14.1 (2016): 955-969. <http://eudml.org/doc/287104>.

@article{JunTaoWang2016,
abstract = {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.},
author = {Jun Tao Wang, Xiao Long Xin, Arsham Borumand Saeid},
journal = {Open Mathematics},
keywords = {Very true MTL-algebra; Subdirectly irreducible; Representation; Stabilizer topology; Very true MTL-logic; very true MTL-algebra; subdirectly irreducible; representation; stabilizer topology; very true MTL-logic},
language = {eng},
number = {1},
pages = {955-969},
title = {Very true operators on MTL-algebras},
url = {http://eudml.org/doc/287104},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Jun Tao Wang
AU - Xiao Long Xin
AU - Arsham Borumand Saeid
TI - Very true operators on MTL-algebras
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 955
EP - 969
AB - 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.
LA - eng
KW - Very true MTL-algebra; Subdirectly irreducible; Representation; Stabilizer topology; Very true MTL-logic; very true MTL-algebra; subdirectly irreducible; representation; stabilizer topology; very true MTL-logic
UR - http://eudml.org/doc/287104
ER -