**Exercises** (due Wednesday, April 23)

- Show that the class of all finite graphs is not first-order axiomatizable (that is, there is no theory $\Sigma$ such that the models of $\Sigma$ are exactly the finite graphs).
- Show that the class of all infinite graphs is not finitely axiomatizable (that is, there is no finite theory $\Sigma$ such that the models of $\Sigma$ are exactly the infinite graphs).

**Supplemental problems**

- $\star$ Show that $\RR$ and $\RR\smallsetminus\{0\}$ are not isomorphic as linear orders.
- $\star\star$ Show that the class of connected graphs is not first-order axiomatizable.
- $\star\star$ Kunen, exercise II.3.8.
- $\star\star$ Kunen, exercise II.13.11.
- $\star\star\star$ Kunen, exercise II.13.12.