Abstract
A polynomially exponential time restrained analytical hierarchy is introduced with the basic properties of the hierarchy followed. And it will be shown that there is a recursive setA such thatA does not belong to any level of thep-arithmetical hierarchies. Then we shall prove that there are recursive setsA andB such that the different levels of the analytical hierarchy relative toA are different and for somen every level higher thann of the analytical hierarchy relative toB is the same as then-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.
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Research supported by the Youth NSF grant JJ890407.
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Sui, Y. The polynomially exponential time restrained analytical hierarchy. J. of Comput. Sci. & Technol. 6, 282–284 (1991). https://doi.org/10.1007/BF02945517
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DOI: https://doi.org/10.1007/BF02945517