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..
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Table of contents: This is an introduction to the
proof theory of arithmetic..
- Fragments of Arithmetic.
Very weak fragments of arithmetic.
Strong fragments of arithmetic.
Fragments of bounded arithmetic.
Sequent calculus formazations of arithmetic.
- Gödel incompleteness.
Arithmetization of metamathematics.
The Gödel incompleteness theorem.
- On the strengths of fragments of arithmetic.
Witnessing theorems for $S^i_2$.
Witnessing theorems and conservations results for $T^i_2$.
Relationships between $B\Sigma_n$ and $I\Sigma_n$.
- Strong incompleteness results for $I\Delta_0 + \exp$.
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