Uniformization and selection over ordinals and trees

We will discuss the uniformization, church synthesis and selection problems
in the monadic second-order theory of ordinals and trees.
We recall the definitions of these problems and survey known results,
including (as time permits):
1. The Shelah-Lifsches results concerning uniformization over the class of
trees.
2. McNaughton's reduction of the Church synthesis problem to $\omega$-length
two person games of perfect information with winning conditions definable by
monadic formulas.
3. Buchi-Landweber's finite-memory determinacy result for these games.
4.  Rabin's tree theorem and basis theorem (which implies selection over the
full binary tree).
5. Gurevich-Shelah's proof that uniformization fails over the tree,
in fact, that there is no definable choice function over the tree.

We will also present some new results concerning selection and games
over countable ordinals longer than $\omega$.
If time permits, we will sketch the proof of some of the above.

No preliminary knowledge is required (it might help a little if you know
what a finite automaton is...)