Kolchin's problems

Kolchin's problems are a set of unsolved problems in differential algebra, outlined by Ellis Kolchin at the International Congress of Mathematicians in 1966

Kolchin Catenary Conjecture

The Kolchin Catenary Conjecture is a fundamental open problem in differential algebra related to dimension theory.

Statement

"Let be a differential algebraic variety of dimension.
By a long gap chain we mean a chain of irreducible differential subvarieties of ordinal number length."
Given an irreducible differential variety of dimension and an arbitrary point, does there exist a long gap chain beginning at and ending at ?
The positive answer to this question is called the Kolchin catenary conjecture.