## Journal of Symbolic Logic

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

Aaron Hill

#### 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 ℕ the collection of trees that have an automorphism under which every node has order exactly n is non-Borel.

#### Article information

Source
J. Symbolic Logic, Volume 77, Issue 1 (2012), 329-336.

Dates
First available in Project Euclid: 20 January 2012

https://projecteuclid.org/euclid.jsl/1327068706

Digital Object Identifier
doi:10.2178/jsl/1327068706

Mathematical Reviews number (MathSciNet)
MR2951644

Zentralblatt MATH identifier
1261.03142

#### Citation

Hill, Aaron. The complexity of squares in the group of isometries of the Baire space. J. Symbolic Logic 77 (2012), no. 1, 329--336. doi:10.2178/jsl/1327068706. https://projecteuclid.org/euclid.jsl/1327068706

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