We consider the positi8ve mu-calculus with successors PmuS, namely a variant of Kozen's modal mu-calculus L sub mu [9] where negation is suppressed and where the basic modalities are a sequence of successor operators l usb 1,..., l sub n, ... In particular we are interested in the sublanguages of P mu s determined by the value of the Emerson-Lei alternation depth [6]. For every n N we exhibit a formula fai sub n whose expression in P mu S requires at leat alternation depth n. IN particular our result gives a new proof of the strict hierarchy theorem for P muS which follows from [1].
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机译：我们考虑带有后继者PmuS的正mu-calculus，即Kozen模态mu-calculus L sub mu [9]的变体，其中否定被抑制，并且基本模态是一系列后继算子l usb 1，...，l sub n，...特别是我们对由Emerson-Lei交替深度值[6]确定的P mu s的子语言感兴趣。对于每n N个，我们展示一个公式fai sub n，其表达式在μμS中要求在跳变深度n处。特别地，我们的结果给出了从[1]开始的P muS严格层次定理的新证明。
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