__Book article:__

** Samuel R. Buss.
"First-Order Proof Theory of Arithmetic."
in **

** Download article: postscript or PDF. **

** 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.

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 $I\Delta_0 + \exp$.