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THE MODEL COMPANION OF DIFFERENTIAL FIELDS WITH FREE OPERATORS

Published online by Cambridge University Press:  29 June 2016

OMAR LEÓN SÁNCHEZ  and
RAHIM MOOSA
OMAR LEÓN SÁNCHEZ
Affiliation:
MCMASTER UNIVERSITY DEPARTMENT OF MATHEMATICS AND STATISTICS 1280 MAIN STREET WEST HAMILTON, ONTARIO L8S 4L8 CANADA E-mail: oleonsan@math.mcmaster.ca
RAHIM MOOSA
Affiliation:
UNIVERSITY OF WATERLOO DEPARTMENT OF PURE MATHEMATICS 200 UNIVERSITY AVENUE WEST WATERLOO, ONTARIO N2L 3G1 CANADA E-mail: rmoosa@uwaterloo.ca
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Abstract

A model companion is shown to exist for the theory of partial differential fields of characteristic zero equipped with free operators that commute with the derivations. The free operators here are those introduced in [R. Moosa and T. Scanlon, Model theory of fields with free operators in characteristic zero, Journal of Mathematical Logic 14(2), 2014]. The proof relies on a new lifting lemma in differential algebra: a differential version of Hensel’s Lemma for local finite algebras over differentially closed fields.

Keywords

03C6012H0512L12differential fielddifference fieldfree operatorsmodel companiondifferential Hensel’s Lemma

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 2 , June 2016 , pp. 493 - 509
Copyright
Copyright © The Association for Symbolic Logic 2016 

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References

REFERENCES

Bustamante, T., Théorie de modèles des corps différentiellement clos avec un automorphisme génerique , PhD Thesis, Université Paris 7, 2005.Google Scholar
Chatzidakis, Z. and Hrushovski, E., Model theory of difference fields . Transactions of the American Mathematical Society, vol. 351 (1999), no. 8, pp. 2997–3071.CrossRefGoogle Scholar
Kolchin, E. R., Differential Algebra and Algebraic Groups, Pure and Applied Mathematics, vol. 54, Academic Press, New York-London, 1973.Google Scholar
Kolchin, E. R., Differential Algebraic Groups, Pure and Applied Mathematics, vol. 114, Academic Press, 1985.Google Scholar
León Sánchez, O., Geometric axioms for differentially closed fields with several commuting derivations . Journal of Algebra, vol. 362 (2012), pp. 107–116. Corrigendum, pp. 332–334.CrossRefGoogle Scholar
León Sánchez, O., On the model companion of partial differential fields with an automorphism. Israel Journal of Mathematics , to appear.Google Scholar
Moosa, R. and Scanlon, T., Jet and prolongation spaces . Journal de l’Institut de Mathématiques de Jussieu, vol. 9 (2010), no. 2, pp. 391–430.Google Scholar
Moosa, R. and Scanlon, T., Model theory of fields with free operators in characteristic zero . Journal of Mathematical Logic, vol. 14 (2014), no. 2, pp. 1450009, 43.CrossRefGoogle Scholar
Rosenfeld, Azriel, Specializations in differential algebra . Transactions of the American Mathematical Society, vol. 90 (1959), pp. 394–407.CrossRefGoogle Scholar
Scanlon, T., A model complete theory of valued D-fields , this Journal, vol. 65 (2000), no. 4, pp. 1758–1784.Google Scholar