  W.Lawvere suggested a approach to differential geometry and to others
mathematical disciplines closed to physics, which allows to give definitions of
derivatives, tangent vectors and tangent bundles without passages to the
limits. This approach is based on a idea of consideration of all settings not
in sets but in some cartesian closed category E, particular in some elementary
topos.
  The synthetic differential geometry (SDG) is the theory developed by A.Kock
in a context of Lawvere's ideas. In a base of the theory is an assumption of
that a geometric line is not a filed of real numbers, but a some nondegenerate
commutative ring R of a line type in E.
  In this work we shall show that SDG allows to develop a Riemannian geometry
and write the Einstein's equations of a field on pseudo-Riemannian formal
manifold. This give a way for constructing a intuitionistic models of general
relativity in suitable toposes.
