Very true operators on MTL-algebras

• Autorzy: Jun Tao Wang , Xiao Long Xin , Arsham Borumand Saeid
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Very true MTL-algebra; Subdirectly irreducible; Representation; Stabilizer topology; Very true MTL-logic

Kategorie tematyczne

• 06F99: None of the above, but in this section
• 03F50: Metamathematics of constructive systems

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 955-969

Daty

wydano

2016-01-01

otrzymano

2016-05-27

zaakceptowano

2016-10-18

online

2016-12-10

Twórcy

autor

Jun Tao Wang

• School of Mathematics, Northwest University, Xi’an, 710127,

autor

Xiao Long Xin

• School of Mathematics, Northwest University, Xi’an, 710127,

autor

Arsham Borumand Saeid

• Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman,

Identyfikatory

DOI

10.1515/math-2016-0086