Representation of perfect and local MV-algebras

Mathematica Slovaca

Ciro Russo¹  Brunella Gerla¹  Luca Spada¹ 

关键词: MV-algebras;    perfect MV-algebras;    representation theorems;    infinitesimal elements;   

DOI  :  10.2478/s12175-011-0015-4

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

We describe representation theorems for local and perfect MV-algebras in terms of ultraproducts involving the unit interval [0, 1]. Furthermore, we give a representation of local Abelian â„“-groups with strong unit as quasi-constant functions on an ultraproduct of the reals. All the above theorems are proved to have a uniform version, depending only on the cardinality of the algebra to be embedded, as well as a definable construction in ZFC.The paper contains both known and new results and provides a complete overview of representation theorems for such classes.

【 授权许可】

Unknown