Open Access
2012/2013 The Descriptive Complexity of Series Rearrangements
Michael P. Cohen
Author Affiliations +
Real Anal. Exchange 38(2): 337-352 (2012/2013).


We consider the descriptive complexity of some subsets of the infinite permutation group \(S_\infty\) which arise naturally from the classical series rearrangement theorems of Riemann, Levy, and Steinitz. In particular, given some fixed conditionally convergent series of vectors in Euclidean space \(\mathbb{R}^d\), we study the set of permutations which make the series diverge, as well as the set of permutations which make the series diverge properly. We show that both collections are \(\boldsymbol\Sigma^0_3\)-complete in \(S_\infty\), regardless of the particular choice of series.


Download Citation

Michael P. Cohen. "The Descriptive Complexity of Series Rearrangements." Real Anal. Exchange 38 (2) 337 - 352, 2012/2013.


Published: 2012/2013
First available in Project Euclid: 27 June 2014

zbMATH: 1304.40001
MathSciNet: MR3261881

Primary: 26A04 , 40A05
Secondary: 40A05

Keywords: and so on , descriptive complexity , series rearrangement %

Rights: Copyright © 2012 Michigan State University Press

Vol.38 • No. 2 • 2012/2013
Back to Top