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Creators/Authors contains: "Moosa, Rahim"

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  1. ; ; (, Journal of the Institute of Mathematics of Jussieu)
    Free, publicly-accessible full text available March 1, 2026
  2. ; (, Journal of the European Mathematical Society)
    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: Thedegree of nonminimalityis 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 theU-rank plus 2. The Borovik–Cherlin conjecture itself is verified for algebraic and meromorphic group actions, and a bound ofU-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. 
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    Free, publicly-accessible full text available February 5, 2026
  3. ; ; (, Journal of Mathematical Logic)
    In this paper, it is shown that if p is a complete type of Lascar rank at least 2, in the theory of differentially closed fields of characteristic zero, then there exists a pair of realisations a, b such that p has a nonalgebraic forking extension over a, b. Moreover, if A is contained in the field of constants then p already has a nonalgebraic forking extension over a. The results are also formulated in a more general setting. 
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  4. ; ; (, Inventiones mathematicae)
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  5. ; (, Advances in Mathematics)
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