so Hensel's lemma for the $\Bbb Z_p$ case states that if you have a polynomial $f \in \Bbb Z_p[X]$ and $r \in \Bbb F_p$ such that $f(r) \equiv 0 \pmod p$ and $f'(r) \ne 0 \pmod p$ then you can lift $r$ all the way to a solution of the polynomial in $\Bbb Z_p$
I ask about 0 and $\aleph_0$ being considered inaccessible cardinals because they arise from the only existential ZFC axioms (empty set and infinity, respectively).
What does " does the algebraic closure of ℚp have a discrete valuation? " mean? Are you asking for any discrete valuation, or that extends the one on $\mathbb{Q}_p$?
if you mean something like $K^*$ mapping to a discrete subgroup of $\mathbb{R}$, and that you define equivalence of valuations by linear scaling, then yes
hello, i have a semi norm $N: \mathbb{R}^n\rightarrow \mathbb{R}$ defined by $N(P)= \sum_{i=1}^m |P(x_i)|$ where P is a polynomial of degree less or equal n, what is the condition to obtain that N is a norm
