Book article:

    Samuel R. Buss.
    "First-Order Proof Theory of Arithmetic."
    in Handbook of Proof Theory, edited by S. R. Buss.
    Elsevier, Amsterdam, 1998, pp 79-147..

    Download article: postscript or PDF

    Table of contents: This is an introduction to the proof theory of arithmetic..

  1. Fragments of Arithmetic.
        Very weak fragments of arithmetic.
        Strong fragments of arithmetic.
        Fragments of bounded arithmetic.
        Sequent calculus formazations of arithmetic.
  2. Gödel incompleteness.
        Arithmetization of metamathematics.
        The Gödel incompleteness theorem.
  3. On the strengths of fragments of arithmetic.
        Witnessing theorems.
        Witnessing theorems for $S^i_2$.
        Witnessing theorems and conservations results for $T^i_2$.
        Relationships between $B\Sigma_n$ and $I\Sigma_n$.
  4. Strong incompleteness results for $I\Delta_0 + \exp$.

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