THE MODEL COMPANION OF DIFFERENTIAL FIELDS WITH FREE OPERATORS

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2016Embargo end date: 01 Aug 2014 United Kingdom English Publisher:Cambridge University Press (CUP)Journal:The Journal of Symbolic Logic, volume 81, pages 493-509 (issn: 0022-4812, eissn: 1943-5886,

Copyright policy )

Authors: Sanchez, Omar; id_orcid 0000-0002-8345-0589; Moosa, Rahim;

doi: 10.1017/jsl.2015.76 , 10.48550/arxiv.1408.1941

arXiv: 1408.1941

THE MODEL COMPANION OF DIFFERENTIAL FIELDS WITH FREE OPERATORS

- Summary
- Subjects
- Metrics

Abstract

AbstractA 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.

Country

United Kingdom

Related Organizations

Keywords

difference field, free operators, differential Hensel's lemma, Model-theoretic algebra, differential field, Mathematics - Logic, Differential algebra, 03C60, 12H05, 12L12, model companion, FOS: Mathematics, Logic (math.LO), Model theory of fields

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	4
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average