Geodesic
A stability criterion
Algebra i logika, Tome 51 (2012) no. 2, pp. 193-196.

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We come up with an independent proof for a corollary to the main theorem in [Yu. L. Ershov, “Stability preservation theorems”, Algebra Logika, 47, No. 3, 269–287 (2008)], since that corollary is the degenerate case of the main theorem (with empty sets $B_0$ and $B_1$), which establishes a stability criterion for a Henselian valued field. Such a proof is given here based on an analysis of tame and purely wild extensions made in [Yu. L. Ershov, “Tame and purely wild extensions of valued fields”, Algebra Analysis, 19, No. 5, 124–136 (2007)].
Keywords: Henselian valued field, stability, tame extension, purely wild extension. 
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Yu. L. Ershov. A stability criterion. Algebra i logika, Tome 51 (2012) no. 2, pp. 193-196. http://geodesic.mathdoc.fr/item/AL_2012_51_2_a2/

[1] Yu. L. Ershov, “Teoremy o sokhranenii stabilnosti”, Algebra i logika, 47:3 (2008), 269–287 | MR | Zbl

[2] Yu. L. Ershov, “Ruchnye i chisto dikie rasshireniya normirovannykh polei”, Algebra i analiz, 19:5 (2007), 124–136 | MR

[3] Yu. L. Ershov, Kratno normirovannye polya, Sib. shkola algebry i logiki, Nauch. kniga, Novosibirsk, 2000