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Published in:
2013 | OriginalPaper | Chapter
Lectures on Proof Theory
Authors : William Ewald, Wilfried Sieg
Published in: David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933
Publisher: Springer Berlin Heidelberg
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The lectures in the Summer Semester of 1920 ended with consistency proofs for extremely weak fragments of arithmetic. The question, made explicit in the Introduction to
Chapter 2
(see p. 296) was then this: Can these consistency proofs somehow be extended to establish the consistency of increasingly stronger and thus mathematically more interesting systems? The lectures of 1921/22 and 1922/23 give a resoundingly positive answer. However, the ‘extensions’ require a remarkable mathematical/logical and methodological breakthrough that leads to Hilbert’s proof theory and his finitist consistency programme.