| Abstract: | 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.
Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 414–420, March, 1998.
The author wishes to thank the participants of the seminar on dynamical systems headed by D. V. Anosov, R. I. Grigorchuk,
and A. M. Stepin as well as the participants of the Kolmogorov seminar of the Mechanics and Mathematics Department of Moscow
State University for discussion of this work. The author is also indebted to N. K. Vereshchagin and A. M. Stepin for support
and valuable remarks as well as to V. V. Ryzhikov for setting the problem and for his assistance. |
