Geometric characterizations of existentially closed fields with operators

Date

2004-12-01

Author

Pierce, D

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This paper concerns the basic model-theory of fields of arbitrary characteristic with operators. Simplified geometric axioms are given for the model-companion of the theory of fields with a derivation. These axioms generalize to the case of several commuting derivations. Let a D-field be a field with a derivation or a difference-operator, called D. The theory of D-fields is companionable. The existentially closed D-fields can be characterized geometrically without distinguishing the two cases in which D can fall. The class of existentially closed fields with a derivation and a difference-operator is elementary only in characteristic 0.

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/64024

Journal

ILLINOIS JOURNAL OF MATHEMATICS

DOI

https://doi.org/10.1215/ijm/1258138514

Collections

Department of Mathematics, Article

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Citation Formats

D. Pierce, “Geometric characterizations of existentially closed fields with operators,” ILLINOIS JOURNAL OF MATHEMATICS, pp. 1321–1343, 2004, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64024.