MathOverflow

We call a binary sequence $s:\mathbb{N}\to\{0,1\}$ disjunctive if every finite binary word appears somewhere in the sequence.
For integers $a, b$ with $a\geq 1, b\geq 0$ we define the strictly increasing function $p_{a,b}:\mathbb{N}\to \mathbb{N}$ by $n\mapsto an+b$....

Given an elementary topos $\mathcal{E}$ for an object $X$, we have the Heyting algebra of its subobjects $Sub(X)$. If $\mathcal{E}$ is a Grothendieck topos, then $Sub(X)$ is complete.
In any case (in an elementary topos $\mathcal{E}$) the subobject classifier $\Omega$ is an internally complete order (see 5.35 p. 147, "Topos theory" by P. Johnstone), but this is slightly different from the statement "any $Sub(X)$ is complete."...

I am looking for matroids in which all minimal basis exchanges look the same, that is, the matroid is transitive on these. Let me explain what I mean by that.
Consider a finite matroid $M$. Define a graph $G_M$ as follows:
The vertices of $G_M$ are the bases of $M$....

Let $K/k$ be an extension of number fields and $H_k$, $H_K$ their respective Hilbert class fields. Is there a transfer map from $\text{Gal}(H_k/k)$ to $\text{Gal}(H_K/K)$?