Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-20T03:27:43.316Z Has data issue: false hasContentIssue false

AN AX-KOCHEN-ERSHOV THEOREM FOR MONOTONE DIFFERENTIAL-HENSELIAN FIELDS

Published online by Cambridge University Press:  01 August 2018

TIGRAN HAKOBYAN*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN URBANA, IL 61801, USAE-mail:hakobya2@illinois.edu

Abstract

Scanlon [5] proves Ax-Kochen-Ershov type results for differential-henselian monotone valued differential fields with many constants. We show how to get rid of the condition with many constants.

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aschenbrenner, M., van den Dries, L., and van der Hoeven, J., Asymptotic Differential Algebra and Model Theory of Transseries, Annals of Mathematics Studies, Princeton University Press, Princeton, NJ, 2017.Google Scholar
Ax, J. and Kochen, S., Diophantine problems over local fields. III. Decidable fields. Annals of Mathematics. Second Series, vol. 83 (1966), pp. 437456.CrossRefGoogle Scholar
Cohn, R., Solutions in the general solution, Contributions to Algebra (Bass, H., Cassidy, P., and Kovacic, J., editors), Academic Press, New York, 1977, pp. 117128.CrossRefGoogle Scholar
Ersov, J., On the elementary theory of maximal normed fields. Soviet Mathematics Doklady, vol. 6 (1965), pp. 13901393.Google Scholar
Scanlon, T., A model complete theory of valued D-fields, this Journal, vol. 65 (2000), no. 4, pp. 1758–1784.Google Scholar