Study on the New Axiomatic Method Giving the Solutions of Hilbert’s 2nd and 6th Problems

In this paper, we propose the new axiomatic method completely different
from old ones.
Thereby we succeeded in giving the definition of the concept of natural
number and solving the problem of its existence. This is the complete
solution of Hilbert’s second problem. As for this, see Ito [4], [24].
Further we give the complete solution of Hilbert’s 6th problem concerning
the natural statistical physics. As for this, see Ito [1]~[3], [5]~[23],
[25], [26].
These solutions are obtained by the new axiomatic method completely
different from Hilbert’s program.
Here we do not need G¨odel’s incompleteness theorem.