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)
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. Kolchin, Ellis Robert, Alexandru Buium, and Phyllis Joan Cassidy. Selected works of Ellis Kolchin with commentary. Vol. 12. American Mathematical Soc., 1999. (pg 607)
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