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Gabriel Ng (University of Manchester)

Category
Models and Sets Seminar
Date
Date
Wednesday 22 February 2023, 2.00 PM
Location
MALL 1

Differentially Large Fields and Taylor Morphisms

Differential largeness is a generalisation of the notion of largeness for pure fields, introduced by Leon-Sanchez and Tressl. This class of differential fields contains many of the model-theoretically tame classes, such as differentially closed fields, closed ordered differential fields, etc. One of the tools that have been developed to study such fields is known as the `twisted Taylor morphism’, which essentially transforms ring homomorphisms into differential ring homomorphisms into the ring of power series in a uniform way. We generalise this notion, and show that differential largeness can also be characterised in terms of generalised Taylor morphisms. If time allows, we will talk about the structure of these generalised Taylor morphisms.