Proof Theory

Cut elimination, ordinal analysis, and Gentzen-style proofs.


foundation tier

Proof Theory. Cut elimination, ordinal analysis, and Gentzen-style proofs.

Foundations and canonical references

The standard treatments of proof theory approach the subject from complementary angles. Troelstra, Basic Proof Theory (2000) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.

Open methodological questions for proof theory include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 2000
    Basic Proof Theory
    troelstra-2000, schwichtenberg-2000

In context

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  1. 01

    Ordinal Analysis

    Measuring consistency strength via ordinal notations.

  2. 02

    Structural Proof Theory

    Linear logic, focusing, and proof normalization.


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