Geodesic
Undecidability of the elementary theory of groups of measure-preserving transformations
Matematičeskie zametki, Tome 63 (1998) no. 3, pp. 414-420 
A. V. Mitin. Undecidability of the elementary theory of groups of measure-preserving transformations. Matematičeskie zametki, Tome 63 (1998) no. 3, pp. 414-420. http://geodesic.mathdoc.fr/item/MZM_1998_63_3_a11/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The undecidability of the elementary theory of the automorphism group for a Lebesgue space is proved. It is shown that arithmetic can be interpreted in this theory. The technique of proof can be carried over to certain other groups.

[1] Khalmosh P. R., Lektsii po ergodicheskoi teorii, Nauka, M., 1959

[2] Fathi A., “Le groupe de transformations de $[0,1]$ qui preservent la mesure de Lebesgue est un groupe simple”, Israel J. Math., 29:2–3 (1978), 302–308 | DOI | MR | Zbl

[3] Eigen S. J., “The group of measure-preserving transformations of $[0,1]$ has no outer automorphisms”, Math. Ann., 259:2 (1982), 259–270 | DOI | MR | Zbl

[4] Ryzhikov V. V., “Predstavlenie preobrazovanii, sokhranyayuschikh meru Lebega, v vide proizvedeniya periodicheskikh preobrazovanii”, Matem. zametki, 38:6 (1985), 860–865 | MR | Zbl

[5] Ershov Yu. L., Lavrov I. A., Taimanov A. D., Taitslin M. A., “Elementarnye teorii”, UMN, 20:4 (1965), 37–108 | MR | Zbl