Proof theory of classical and intuitionistic logic

In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press (2008)
Abstract
This chapter focuses on the development of Gerhard Gentzen's structural proof theory and its connections with intuitionism. The latter is important in proof theory for several reasons. First, the methods of Hilbert's old proof theory were limited to the “finitistic” ones. These methods proved to be insufficient, and they were extended by infinitistic principles that were still intuitionistically meaningful. It is a general tendency in proof theory to try to use weak principles. A second reason for the importance of intuitionism for proof theory is that the proof-theoretical study of intuitionistic logic has become a prominent part of logic, with applications in computer science.
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Reprint years 2009
DOI 10.1093/acprof:oso/9780195137316.003.0033
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