The variety generated by all the ordinal sums of perfect MV-chains

From Mathfuzzlog
Jump to: navigation, search
Authors:
Matteo Bianchi
Title: The variety generated by all the ordinal sums of perfect MV-chains
Journal: Studia Logica
Volume 101
Number 1
Pages: 11-29
Year: 2013
Download from the publisher





Abstract

We present the logic Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle BL_{Chang}} , an axiomatic extension of BL (see [23]) whose corresponding algebras form the smallest variety containing all the ordinal sums of perfect MV-chains. We will analyze this logic and the corresponding algebraic semantics in the propositional and in the first-order case. As we will see, moreover, the variety of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle BL_{Chang}} -algebras will be strictly connected to the one generated by Chang’s MV-algebra (that is, the variety generated by all the perfect MV-algebras): we will also give some new results concerning these last structures and their logic.