Jan Johannsen's Fragments of Arithmetic Page
## Fragments of Arithmetic - Lecture Notes

I have written a short text (23 pages) about Fragments of Arithmetic
for the participants of a seminar, in German.
It concentrates on Bounded Induction ($I\Delta_0$) and Open Induction ($IE_0$).
I plan to expand this sometimes in the future.
Below you see the (current) Table of Contents.

### Fragments of Arithmetic

- Preliminaries
- Nonstandard models of arithmetic
- Order-type of nonstandard models
- Many models of $Th(\Nat)$
- The axiom system $PA^-$
- The arithmetical hierarchy
- Absoluteness of $\Delta_0$-formulas
- Parikh's theorem
- Some interesting facts about $I\Delta_0$
- A model-theoretic formulation of induction
- Overspill
- Tennenbaum's theorem for $I\Delta_0$
- The bounded arithmetic hierarchy
- Shepherdson's model construction
- $IE_0$ is not finitely axiomatizable

If you like to have a copy, send me email.