scholarly journals The model theory of differential fields of characteristic $p\not=0$

1973 ◽  
Vol 40 (2) ◽  
pp. 577-577
Author(s):  
Carol Wood
Keyword(s):  
Model Theory ◽  
Characteristic P ◽  
Differential Fields

Differential forms in the model theory of differential fields

2003 ◽  
Vol 68 (3) ◽  
pp. 923-945 ◽  
Author(s):  
David Pierce
Keyword(s):  
Differential Geometry ◽  
Model Theory ◽  
Characteristic Zero ◽  
Differential Forms ◽  
Main Tool ◽  
Frobenius Theorem ◽  
Lie Bracket ◽  
Existentially Closed ◽  
Differential Fields

AbstractFields of characteristic zero with several commuting derivations can be treated as fields equipped with a space of derivations that is closed under the Lie bracket. The existentially closed instances of such structures can then be given a coordinate-free characterization in terms of differential forms. The main tool for doing this is a generalization of the Frobenius Theorem of differential geometry.

scholarly journals Imaginaries and invariant types in existentially closed valued differential fields

2019 ◽  
Vol 2019 (750) ◽  
pp. 157-196 ◽  
Author(s):  
Silvain Rideau
Keyword(s):  
Model Theory ◽  
Extension Property ◽  
Valued Fields ◽  
Invariant Extension ◽  
Open Questions ◽  
Existentially Closed ◽  
Differential Fields ◽  
Abstract Criterion

Abstract We answer three related open questions about the model theory of valued differential fields introduced by Scanlon. We show that they eliminate imaginaries in the geometric language introduced by Haskell, Hrushovski and Macpherson and that they have the invariant extension property. These two results follow from an abstract criterion for the density of definable types in enrichments of algebraically closed valued fields. Finally, we show that this theory is metastable.

Joseph Becker and Leonard Lipshitz. Remarks on the elementary theories of formal and convergent power series. Fundament a mathematicae, vol. 105 (1980), pp. 229–239. - Françoise Delon. Indécidabilité de la théorie des anneaux de séries formelles à plusiers indéterminées. Fundament a mathematicae, vol. 112 (1981), pp. 215–229. - J. Becker, J. Denef, and L. Lipshitz. Further remarks on the elementary theory of formal power series rings. Model theory of algebra and arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic held at Karpacz, Poland, September 1–7, 1979, edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture notes in mathematics, vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, pp. 1–9. - Françoise Delon. Hensel fields in equal characteristic p > 0. Model theory of algebra and arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic held at Karpacz, Poland, September 1–7, 1979, edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture notes in mathematics, vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, pp. 108–116.

1985 ◽  
Vol 50 (3) ◽  
pp. 853-854
Author(s):  
S. Basarab
Keyword(s):  
New York ◽  
Power Series ◽  
Model Theory ◽  
Elementary Theory ◽  
Convergent Power Series ◽  
Characteristic P ◽  
Lecture Notes ◽  
Power Series Rings ◽  
Formal Power ◽  
Elementary Theories

Angus Macintyre, Kenneth McKenna, and Lou van den Dries. Elimination of quantifiers in algebraic structures. Advances in mathematics, vol. 47 (1983), pp. 74–87. - L. P. D. van den Dries. A linearly ordered ring whose theory admits elimination of quantifiers is a real closed field. Proceedings of the American Mathematical Society, vol. 79 (1980), pp. 97–100. - Bruce I. Rose. Rings which admit elimination of quantifiers. The journal of symbolic logic, vol. 43 (1978), pp. 92–112; Corrigendum, vol. 44 (1979), pp. 109–110. - Chantal Berline. Rings which admit elimination of quantifiers. The journal of symbolic logic, vol. 43 (1978), vol. 46 (1981), pp. 56–58. - M. Boffa, A. Macintyre, and F. Point. The quantifier elimination problem for rings without nilpotent elements and for semi-simple rings. Model theory of algebra and arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic held at Karpacz, Poland, September 1–7, 1979, edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture notes in mathematics, vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, pp. 20–30. - Chantal Berline. Elimination of quantifiers for non semi-simple rings of characteristic p. Model theory of algebra and arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic held at Karpacz, Poland, September 1–7, 1979, edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture notes in mathematics, vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, pp. 10–19.

1985 ◽  
Vol 50 (4) ◽  
pp. 1079-1080
Author(s):  
Gregory L. Cherlin
Keyword(s):  
New York ◽  
Model Theory ◽  
American Mathematical Society ◽  
Quantifier Elimination ◽  
Symbolic Logic ◽  
Closed Field ◽  
Characteristic P ◽  
Lecture Notes ◽  
Ordered Ring ◽  
Elimination Problem
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