Logic Seminar
Nigel Pynn-Coates
University of Vienna
Differential-algebraic dimension in transserial tame pairs
Abstract: The theory of closed H-fields is model complete and axiomatizes the
theory of transseries and maximal Hardy fields, as Aschenbrenner, Van
den Dries, and Van der Hoeven have shown in a long series of works. To
better understand large closed H-fields, such as maximal Hardy fields, I
recently extended this model completeness to the theory of tame pairs of
closed H-fields. Building on this work, I will explain how to extend
differential-algebraic dimension on a closed H-field to tame pairs of
closed H-fields so that it is a fibred dimension function in the sense
of [L. van den Dries, "Dimension of definable sets, algebraic
boundedness and Henselian fields", Ann. Pure Appl. Logic 45.2 (1989),
189–209] and the nonempty dimension zero definable sets are exactly the
nonempty discrete definable sets. The model-theoretic notion of
coanalyzability will also make an appearance.
Tuesday April 29, 2025 at 3:30 PM in 636 SEO