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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 4L8CANADAE-mail:[email protected]
RAHIM MOOSA
Affiliation:
UNIVERSITY OF WATERLOO DEPARTMENT OF PURE MATHEMATICS 200 UNIVERSITY AVENUE WEST WATERLOO, ONTARIO N2L 3G1CANADAE-mail:[email protected]
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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
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

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