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Preprint Number 1387

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1387. Allen Gehret and Elliot Kaplan
Distality for the asymptotic couple of the field of logarithmic transseries
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Submission date: 15 February 2018

Abstract:

We show that the theory T_{log} of the asymptotic couple of the field of logarithmic transseries is distal. As distal theories are NIP (= the non-independence property), this provides a new proof that T_{log} is NIP. Finally, we show that T_{log} is not strongly NIP, and in particular, it is not dp-minimal and it does not have finite dp-rank.

Mathematics Subject Classification: Primary 03C64, Secondary 03C45, 06F20

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Full text arXiv 1802.05732: pdf, ps.


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