bundles without passages to the limits. This approach is based on an idea of consideration generalized or [*variable sets*]{} which are the objects of some cartesian closed category $\E$, in particular, of some elementary topos.

The definition of these categories was given by Lawvere and Tirne. They are possessed of their own inner logic, which in general are intuitionistic. So it is possible to formulate mathematical theories with the help of some common logical language and to give proofs of theorems using the laws of intuitionistic logic.

The synthetic differential geometry (SDG) is the theory which was developed by A.Kock [@Ko] in the context of the Lawrere’s ideas. Basis of this theory is the assumption that a geometric line is not a filled of real numbers, but is some nondegenerate commutative ring $R$ of a line type, i.e such that it satisfies the following axiom:

. [*Let $D =\{ x\in R \ |\ x^2=0 \}$. For every $g:D\rightarrow R$ there exist the unique $a, b\in R$, such that for any $ d\in D$ the equation $g(d)=a+d\cdot b$ is valid.*]{}

It follows from this axiom that all functions $f:R\rightarrow R$ have the first derivatives.

Further we assume another axioms with respect 