![[1245] Model theory, differential algebra and functional transcendence](/media/cache/video_light/uploads/video/SeminaireBourbaki.jpg)
publiée le 9 décembre 2025
[1245] Model theory, differential algebra and functional transcendence
De Amador Martin-Pizarro
The ordered differential field of transseries
Apparaît dans la collection : Ordered algebraic structures and related topics / Structures algébriques ordonnées et leurs interactions
The field of Laurent series (with real coefficients, say) has a natural derivation but is too small to be closed under integration and other natural operations such as taking logarithms of positive elements. The field has a natural extension to a field of generalized series, the ordered differential field of transseries, where these defects are remedied in a radical way. I will sketch this field of transseries. Recently it was established (Aschenbrenner, Van der Hoeven, vdD) that the differential field of transseries also has very good model theoretic properties. I hope to discuss this in the later part of my talk.
