The polynomially exponential time restrained analytical hierarchy (Q1337640)

The author defines a \(p\)-analytical hierarchy of relations \(\Sigma^{1,p} [n]\) and \(\Pi^{1,p} [n]\) making some mistakes through carelessness in definitions. A series of simple properties of the hierarchy are given generalizing those of the well-known analytical hierarchy. Then the author shows that there exists a (recursive) oracle \(A\) such that the sentence `\(\Sigma^{1,p} [n] [A]= \Sigma^{1,p} [n+1] [A]\)' is neither provable nor disprovable in ZF.