Abstract
We present finitary formulations of two well known results concerning infinite series, namely Abel's theorem, which establishes that if a series converges to some limit then its Abel sum converges to the same limit, and Tauber's theorem, which presents a simple condition under which the converse holds. Our approach is inspired by proof theory, and in particular Gödel's functional interpretation, which we use to establish quantitative versions of both of these results.
| Original language | English |
|---|---|
| Pages (from-to) | 300-310 |
| Number of pages | 11 |
| Journal | Mathematical Logic Quarterly |
| Volume | 66 |
| Issue number | 3 |
| Early online date | 28 Sept 2020 |
| DOIs | |
| Publication status | Published - 7 Oct 2020 |
Bibliographical note
Funding Information:This work was supported by the German Science Foundation (DFG Project KO 1737/6‐1). The author is grateful to the anonymous referee for their valuable suggestions, particularly their encouragement to clarify the underlying proof theory.
Publisher Copyright:
© 2020 The Authors. Mathematical Logic Quarterly published by Wiley-VCH GmbH
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
Funding
This work was supported by the German Science Foundation (DFG Project KO 1737/6‐1). The author is grateful to the anonymous referee for their valuable suggestions, particularly their encouragement to clarify the underlying proof theory.
ASJC Scopus subject areas
- Logic