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Preprint Number 2694
2694. Nigel Pynn-Coates Tame pairs of transseries fields E-mail: Submission date: 13 August 2024 Abstract:
This paper concerns pairs of models of the theory of the differential field
of logarithmic-exponential transseries that are tame as a pair of real closed
fields. That is, the smaller model is bounded inside the larger model and there
exists a standard part map. This covers for instance the differential fields of
hyperseries or surreal numbers or maximal Hardy fields equipped with suitable
enlargements of the differential field of transseries. The theory of such pairs
is complete and model complete in a natural language and it has quantifier
elimination in the same language expanded by two predicates and a standard part
map. Additionally, the smaller model is purely stably embedded in the pair, and
hence so is the constant field. Mathematics Subject Classification: Keywords and phrases: |
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