Abstract
The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have a definable choice function (by a monadic formula with parameters)? A natural dichotomy arises where the trees that fall in the first class don't have a definable choice function and the trees in the second class have even a definable well ordering of their elements. This has a close connection to the uniformization problem.
| Original language | English |
|---|---|
| Pages (from-to) | 1206-1227 |
| Number of pages | 22 |
| Journal | Journal of Symbolic Logic |
| Volume | 61 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 1996 |