THE MODEL COMPANION OF DIFFERENTIAL FIELDS WITH FREE OPERATORS. (29th June 2016)

• Record Type: Journal Article
• Authors: SÁNCHEZ, OMAR LEÓN; MOOSA, RAHIM
• Is Part Of: Journal of symbolic logic. Volume 81:Number 2(2016)
• Page Start: 493
• Page End: 509
• Publication Date: 2016-06-29
• Subjects: 03C60, -- 12H05, -- 12L12; differential field, -- difference field, -- free operators, -- model companion, -- differential Hensel's Lemma; Logic, Symbolic and mathematical -- Periodicals; 511.3
• DOI: 10.1017/jsl.2015.76
• Languages: English
• ISSNs: 0022-4812

Abstract

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.