Invariant measures in free MV-algebras
| dc.creator | Panti, Giovanni | |
| dc.date | 2005-08-24 | |
| dc.date | 2007-04-20 | |
| dc.date.accessioned | 2026-07-07T07:57:25Z | |
| dc.date.available | 2026-07-07T07:57:25Z | |
| dc.description | MV-algebras can be viewed either as the Lindenbaum algebras of Lukasiewicz infinite-valued logic, or as unit intervals of lattice-ordered abelian groups in which a strong order unit has been fixed. The free n-generated MV-algebra Free_n is representable as an algebra of continuous piecewise-linear functions with integer coefficients over the unit cube [0,1]^n. The maximal spectrum of Free_n is canonically homeomorphic to [0,1]^n, and the automorphisms of the algebra are in 1-1 correspondence with the pwl homeomorphisms with integer coefficients of the unit cube. In this paper we prove that the only probability measure on [0,1]^n which is null on underdimensioned 0-sets and is invariant under the group of all such homeomorphisms is the Lebesgue measure. From the viewpoint of lattice-ordered abelian groups, this fact means that, in relevant cases, fixing an automorphism-invariant strong unit implies fixing a distinguished probability measure on the maximal spectrum. From the viewpoint of algebraic logic, it means that the only automorphism-invariant truth averaging process that detects pseudotrue propositions is the integral with respect to Lebesgue measure. | |
| dc.description | 12 pages, 4 figures. Title changed, motivational section rewritten, mathematics unchanged. To appear in Communications in Algebra | |
| dc.identifier | https://arxiv.org/abs/math/0508445 | |
| dc.identifier | http://arxiv.org/abs/math/0508445 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127643 | |
| dc.subject | Logic | |
| dc.subject | Dynamical Systems | |
| dc.subject | 06D35; 37A05 | |
| dc.title | Invariant measures in free MV-algebras | |
| dc.type | text |