# The meaning of some asymptotic notation

I am trying to make sense of some notation in a paper I am reading. In particular, in the following excerpt, I've circled the notation that I do not understand:

This is a restatement of a theorem in an earlier paper in which this particular notation does not appear, but rather it is assumed that $$k \ll t \ll v$$. So my guess is that $$t \geq t_o(k)$$ captures $$k \ll t$$ and $$v \geq v_o(k,t)$$ captures $$t \ll v$$ and $$k \ll v$$, though I'm not too sure. What is the correct way of interpreting this kind of notation?

It's not very clear, but I would interpret it as meaning that there exists some $$t_0$$ depending only on $$k$$ such that for every $$t\geq t_0$$ we can find $$v_0$$ (depending on both $$t$$ and $$k$$) such that the statement is true for every $$k$$-uniform hypergraph with maximum degree bounded by $$t^{k-1}$$ and at least $$v_0$$ vertices.
This is also how I would interpret $$k\ll t\ll v$$ assuming that it's clear that the dependency goes in that direction¹ and the person who wrote it is doing combinatorics - I think that could mean something quite different in other areas of mathematics.
¹ that is, as opposed to $$v$$ being the basic quantity with $$t$$ and $$k$$ having to be sufficiently small.