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

  • TIGRAN HAKOBYAN (a1)

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.

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[1]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.
[2]Ax, J. and Kochen, S., Diophantine problems over local fields. III. Decidable fields. Annals of Mathematics. Second Series, vol. 83 (1966), pp. 437456.
[3]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.
[4]Ersov, J., On the elementary theory of maximal normed fields. Soviet Mathematics Doklady, vol. 6 (1965), pp. 13901393.
[5]Scanlon, T., A model complete theory of valued D-fields, this Journal, vol. 65 (2000), no. 4, pp. 1758–1784.

Keywords

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

  • TIGRAN HAKOBYAN (a1)

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