Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778136 | Annals of Pure and Applied Logic | 2017 | 20 Pages |
Abstract
Differently from boolean logic, in Åukasiewicz infinite-valued propositional logic Åâ the theory Îmaxâ¡,v consisting of all formulas satisfied by a model vâ[0,1]n is not the only one having v as its unique model: indeed, there is a smallest such theory Îminâ¡,v, the germinal theory at v, which in general is strictly contained in Îmaxâ¡,v. The Lindenbaum algebra of Îmaxâ¡,v is promptly seen to coincide with the subalgebra of the standard MV-algebra [0,1] generated by the coordinates of v. The description of the Lindenbaum algebras of germinal theories in two variables is our main aim in this paper. As a basic prerequisite of independent interest, we prove that for any models v and w the germinal theories Îminâ¡,v and Îminâ¡,w have isomorphic Lindenbaum algebras iff v and w have the same orbit under the action of the affine group over the integers.
Related Topics
Physical Sciences and Engineering
Mathematics
Logic
Authors
Leonardo Manuel Cabrer, Daniele Mundici,