Speaker: Omar Leon-Sanchez，University of Manchester, UK

Inviter: Wei Li

Title: Some remarks on differentially large fields and closed ordered differential fields

Language: Chinese

Time & Venue: 2024.07.05 10:00-11:00 思源楼 813

Abstract: We will give a brief introduction and overview of some recent results on differentially large fields (in characteristic zero). In particular, we note that a field admits a differentially large structure iff it is of infinite transcendence degree (over ℚ). We also give conditions on when a differential field can be extended to a differentially large one without changing the constants. 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. Time permitting, we will discuss the question of when a real closed differential field has a CODF extension inside a differential closure. This is joint work with Marcus Tressl.