The space $\beta N$ and the continuum hypothesis

Gillman, L.

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We prove some properties similar to the theorem Ax-Kochen-Ershov, in some cases of pairs of algebraically maximal fields of residue characteristic p > 0. This properties hold in particular for pairs of Kaplansky fields of equal characteristic, formally p-adic fields and finitely ramified fields. From that we derive results about decidability of such extensions.