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.