The Descriptive Complexity of Series Rearrangements
نویسنده
چکیده
We consider the descriptive complexity of some subsets of the infinite permutation group S∞ 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 Rd, 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 Σ3-complete in S∞, regardless of the particular choice of series.
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