2021/06/04 by James Freitag, Freitag, James, Rahim Moosa +1 · 4 citations
Mathematics · #03C45 #12H05 #14L30 #32J99 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2106.02537
openalex publication_date 2021/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the search for methods to establish strong minimality of certain low order algebraic differential equations, a measure of how far a finite rank stationary type is from being minimal is introduced and studied: The \em degree of nonminimality is the minimum number of realisations of the type required to witness a nonalgebraic forking extension. Conditional on the truth of a conjecture of Borovik and Cherlin on the generic multiple-transitivity of homogeneous spaces definable in the stable theory being considered, it is shown that the nonminimality degree is bounded by the U-rank plus 2. The Borovik-Cherlin conjecture itself is verified for algebraic and meromorphic group actions, and a bound of U-rank plus 1 is then deduced unconditionally for differentially closed fields and compact complex manifolds. An application is given regarding transcendence of solutions to algebraic differential equations.