The Polynomially Exponential Time Restrained Analytical Hierarchy

A polynomially exponential time restrained analytical hierarchy is introduced with the basic proper ties of the hierarchy followed.And it will be shown that there is a recursive set A such that A does not belong to any level of the p-arithmetical hierarchies.Then we shall prove that there are recursive sets A and B such that the different levels of the analytical hierarchy relative to A are different and for some n every level higher than n of the analytical hierarchy relative to B is the same as the n-th l…