Subfields of henselian valued fields
Let $(K,v)$ be a henselian valued field of arbitrary rank which is not separably closed. Let $k$ be a subfield of $K$ of finite codimension and $v_k$ be the valuation obtained by restricting $v$ to $k$. We give some necessary and sufficient conditions for $(k,v_k)$ to be henselian. In particular, it is shown that if $k$ is dense in its henselization, then $(k,v_k)$ is henselian. We deduce some well known results proved in this direction through other considerations.