摘要
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 level. And whether the higher levels are collapsed into some lower level is neither provable nor disprovable in set theory and several other results.
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 level. And whether the higher levels are collapsed into some lower level is neither provable nor disprovable in set theory and several other results.
基金
Research supported by the Youth NSF grant JJ890407.
