The complexity of squares in the group of isometries of the Baire space

Journal of Symbolic Logic 77 (1):329-336 (2012)
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Abstract

We prove that in the Polish group of isometries of the Baire space the collection of n-th powers is non-Borel. We also prove that in the Polish space of trees on $\mathbb{N}$ the collection of trees that have an automorphism under which every node has order exactly n is non-Borel

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10.2178/jsl/1327068706

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