Journal
MATHEMATICAL LOGIC QUARTERLY
Volume 66, Issue 3, Pages 300-310Publisher
WILEY-V C H VERLAG GMBH
DOI: 10.1002/malq.201900076
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Funding
- German Science Foundation (DFG) [KO 1737/6-1]
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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 Godel's functional interpretation, which we use to establish quantitative versions of both of these results.
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