C. U. Jensen suggested the following construction, starting from a field $K: K_0 = K, K_{\alpha + 1} = K_\alpha ((X_\alpha)), K_\alpha = \bigcup K_\beta$ if $\alpha$ is limit and asked when two fields $k_\alpha$ and $K_\beta$ are equivalent. We give a complete answer in the case of a field $K$ of characteristic 0.
Publié le : 1986-06-14
Classification:
Ax/Kochen-Ersov theorem,
definability of valuations in the language of rings,
elementary equivalence,
elementary inclusion,
first-order theories,
iterated power series fields,
generalized power series fields,
periodicity
@article{1183742099,
author = {Delon, Francoise},
title = {Periodicite Des Theories Elementaires Des Corps De Series Formelles Iterees},
journal = {J. Symbolic Logic},
volume = {51},
number = {1},
year = {1986},
pages = { 334-351},
language = {fr},
url = {http://dml.mathdoc.fr/item/1183742099}
}
Delon, Francoise. Periodicite Des Theories Elementaires Des Corps De Series Formelles Iterees. J. Symbolic Logic, Tome 51 (1986) no. 1, pp. 334-351. http://gdmltest.u-ga.fr/item/1183742099/