## Godel's
theorem as a corollary of impossibility of complete axiomatization of geometry

## Yuri A. Rylov

*Institute for Problems in Mechanics, Russian
Academy of Sciences*

* 101-1 ,Vernadskii Ave., Moscow, 119526, Russia*

* email: rylov@ipmnet.ru*

Web site: http://rsfq1.physics.sunysb.edu/~rylov/yrylov.htm

or mirror Web site: http://gasdyn-ipm.ipmnet.ru/~rylov/yrylov.htm

Updated September 1,
2007

#### abstract

Not any
geometry can be axiomatized. The paradoxical Godel's theorem starts from the
supposition that any geometry can be axiomatized and goes to the result, that
not any geometry can be axiomatized. One considers example of two close
geometries (Riemannian geometry and $\sigma $-Riemannian one), which are
constructed by different methods and distinguish in some details. The
Riemannian geometry reminds such a geometry, which is only a part of the full
geometry. Such a possibility is covered by the Godel's theorem.

There is
text of the paper in English (pdf, ps) and in Russian (ps, pdf)