Proof theory and set theory

Synthese 62 (2):255 - 263 (1985)
Abstract
The foundations of mathematics are divided into proof theory and set theory. Proof theory tries to justify the world of infinite mind from the standpoint of finite mind. Set theory tries to know more and more of the world of the infinite mind. The development of two subjects are discussed including a new proof of the accessibility of ordinal diagrams. Finally the world of large cardinals appears when we go slightly beyond girard's categorical approach to proof theory
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DOI 10.1007/BF00486049
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Michael Rathjen (1994). Proof Theory of Reflection. Annals of Pure and Applied Logic 68 (2):181-224.
Mariko Yasugi (1989). The Machinery of Consistency Proofs. Annals of Pure and Applied Logic 44 (1-2):139-152.

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