Journal of Symbolic Logic 51 (2):334-351 (1986)

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
Keywords 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
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DOI 10.2307/2274057
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