Logic Seminar: Differential-algebraic dimension in transserial tame pairs, by Nigel Pynn-Coates
April 29, 2025
3:30 PM - 4:20 PM
Nigel Pynn-Coates (University of Vienna): Differential-algebraic dimension in transserial tame pairs
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),
189209] 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.
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Date posted
Apr 14, 2025
Date updated
Apr 14, 2025
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