Bernoulli automorphisms of finitely generated free MV-algebras |
| |
Authors: | Giovanni Panti |
| |
Institution: | Department of Mathematics and Computer Science, University of Udine, Via delle Scienze 208, 33100 Udine, Italy |
| |
Abstract: | MV-algebras can be viewed either as the Lindenbaum algebras of ?ukasiewicz 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, in 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. |
| |
Keywords: | 06D35 37A05 |
本文献已被 ScienceDirect 等数据库收录! |
|