Effective definability of Kolchin polynomials
While the natural model-theoretic ranks available in differentially closed fields (of characteristic zero), namely Lascar and Morley rank, are known not to be definable in families of differential varieties; in this note we show that the differential-algebraic rank given by the Kolchin polynomial is...
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Veröffentlicht in: | Proceedings of the American Mathematical Society 2020-04, Vol.148 (4), p.1455-1466 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | While the natural model-theoretic ranks available in differentially closed fields (of characteristic zero), namely Lascar and Morley rank, are known not to be definable in families of differential varieties; in this note we show that the differential-algebraic rank given by the Kolchin polynomial is in fact definable. As a byproduct, we are able to prove that the property of being weakly irreducible for a differential variety is also definable in families. The question of full irreducibility remains open; it is known to be equivalent to the generalized Ritt problem. |
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ISSN: | 0002-9939 1088-6826 |
DOI: | 10.1090/proc/14869 |