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

摘要

Not any geometry can be axiomatized. The paradoxical Godel's theorem startsfrom the supposition that any geometry can be axiomatized and goes to theresult, that not any geometry can be axiomatized. One considers example of twoclose geometries (Riemannian geometry and $\sigma $-Riemannian one), which areconstructed by different methods and distinguish in some details. TheRiemannian geometry reminds such a geometry, which is only a part of the fullgeometry. Such a possibility is covered by the Godel's theorem.