Some remarks on differentially large fields and CODFs

Abstract: We make some observations around differentially large fields (in characteristic zero). In particular, we note that they can be characterised as those differential fields that are existentially closed in the "differential algebraic" Laurent series ring. We also note that a field admits a differentially large structure iff it is of infinite transcendence degree (over Q). We then turn our attention to the theory CODF (closed ordered differential fields). We observe that a real closed differential field has a prime model extension (in CODF) iff it is already a CODF. This extends a result of Singer showing that CODF has no prime model. We then discuss the question of when a real closed differential field has a CODF extension inside a differential closure. This is a combination of joint work with Marcus Tressl and Anand Pillay.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.