Geodesic
Undecidability of the elementary theory of groups of measure-preserving transformations
Matematičeskie zametki, Tome 63 (1998) no. 3, pp. 414-420.

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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. 
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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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