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Preprint Number 1672

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1672. Nigel Pynn-Coates
A model complete theory of pre-H-fields with gap 0

Submission date: 27 October 2019


The theory of differential-henselian, real closed pre-H-fields that have exponential integration and closed ordered differential residue field has quantifier elimination and is the model completion of the theory of pre-H-fields with gap 0. From quantifier elimination, we deduce that this theory has NIP. Moreover, when the ordered differential residue field, instead of being a closed ordered differential field, is a structure in some language expanding that of ordered differential rings whose theory is model complete, the corresponding two-sorted theory is model complete.

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Full text arXiv 1910.12171: pdf, ps.

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