Abstract
In this paper, we look at strongly minimal sets definable in a differentially closed field of characteristic 0. In [3], Hrushovski and Sokolović show that such sets are essentially Zariski geometries. Thus either thre is a definable strongly minimal field nonorthogonal to $D$, or $D$ is locally modular and nontrivial, or $D$ is trivial. We show that the strongly minimal sets defined by a certain family of differential equations are trivial. We also prove a theorem wich provides a test for the orthogonality of types over an ordinary differential field.
Citation
Tracey McGrail. "The search for trivial types." Illinois J. Math. 44 (2) 263 - 271, Summer 2000. https://doi.org/10.1215/ijm/1255984840
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