Undecidability of the elementary theory of groups of measure-preserving transformations
type: Item
instance of: scholarly article
title: Undecidability of the elementary theory of groups of measure-preserving transformations
zbMATH Open document ID: 0920.28014
DOI: 10.1007/BF02317783
published in: Mathematical Notes
publication date: 1999-08-15T00:00:00Z
review text: Let \(G\) be the group of invertible transformations of \((0,1)\) preserving the Lebesgue measure. Two transformations are equal if they differ only on a set of measure zero. Let \(L\) be the language of group theory containing variables \(f,g,\ldots\) for elements of the group, the group product \(fg\) (composition), the equality \(f=g\), connectives and quantifiers. Theorem: There is a translation (effective procedure) that for any closed arithmetic formula produces a closed formula in \(L\) which is true if and only if the arithmetic formula is. Corollary: The elementary theory of groups of measure-preserving transformations is nonsolvable.
Mathematics Subject Classification ID: 28D15
Mathematics Subject Classification ID: 03B25
zbMATH DE Number: 1262565
zbMATH Keywords: group of measure-preserving transformations
zbMATH Keywords: nonsolvability
author: Alexander V. Mitin
MaRDI profile type: Publication
cites work: Q3234755
cites work: Le groupe des transformations de \([0,1]\) qui preservent la mesure de Lebesgue est un groupe simple
cites work: Representation of transformations preserving the Lebesgue measure in the form of a product of periodic transformations
cites work: Q5596785
description: scientific article; zbMATH DE number 1262565