Bernoulli automorphisms of finitely generated free MV-algebras
| dc.creator | Panti, Giovanni | |
| dc.date | 2004-08-26 | |
| dc.date | 2006-01-28 | |
| dc.date.accessioned | 2026-07-07T06:38:45Z | |
| dc.date.available | 2026-07-07T06:38:45Z | |
| dc.description | MV-algebras can be viewed either as the Lindenbaum algebras of Lukasiewicz infinite-valued logic, or as unit intervals [0,u] of lattice-ordered abelian groups in which a strong order unit u>0 has been fixed. They form an equational class, and the free n-generated free MV-algebra is representable as an algebra of piecewise-linear continuous functions with integer coefficients over the unit n-dimensional cube. In this paper we show that the automorphism group of such a free algebra contains elements having strongly chaotic behaviour, is the sense that their duals are measure-theoretically isomorphic to a Bernoulli shift. This fact is noteworthy from the viewpoint of algebraic logic, since it gives a distinguished status to Lebesgue measure as an averaging measure on the space of valuations. As an ergodic theory fact, it provides explicit examples of volume-preserving homeomorphisms of the unit cube which are piecewise-linear with integer coefficients, preserve the denominators of rational points, and enjoy the Bernoulli property. | |
| dc.description | 12 pages, 3 figures. Revised version according to the referee's suggestions. To appear in the J. of Pure and Applied Algebra | |
| dc.identifier | https://arxiv.org/abs/math/0408370 | |
| dc.identifier | http://arxiv.org/abs/math/0408370 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100851 | |
| dc.subject | Logic | |
| dc.subject | Dynamical Systems | |
| dc.subject | 06D35; 37A05 | |
| dc.title | Bernoulli automorphisms of finitely generated free MV-algebras | |
| dc.type | text |