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

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

, does there exist a long gap chain beginning at

The positive answer to this question is called the Kolchin catenary conjecture.