Proof theory was established at first by David Hilbert to gain a foundation of classical mathematics by very elementary methods which he called finitary (finit). The idea was to formalize the particular parts of classical mathematics and to prove the consistency of the corresponding formal systems only in a syntactical way without reference to the intended meanings of the formal systems.
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- Hilbert, D. and Bernays, P., Grundlagen der Mathematik I, II, Springer-Verlag, Heidelberg, New York 1968, 1970.Google Scholar
- Schütte, K., Proof Theory, Springer-Verlag, Berlin, Heidelberg, New York 1977.Google Scholar
- Spector, C., ‘Provably Recursive Functional of Analysis: A Consistency Proof of Analysis by an Extension of Principles Formulated in Current Intuitionistic Mathematics’, Proc. Symp. Pure Math. AMS V (1962), 1–27.Google Scholar
- Takeuti, G., Proof Theory, North-Holland Publ. Co., Amsterdam 1975.Google Scholar