What is the meaning of 'uniform' in Blum's paper "On the Size of Machines" In Blum's &quot;On the Size of Machines&quot; he uses the word 'uniform' in several places.
For instance, in Theorem 1, he writes

Let $f$ be any recursive function. Then there exists $i,j\in \mathbb{N}$, both uniform in $f$,$g$ such that...

What does the word 'uniform' mean in this context?
In addition, is there a reference that defines what it means when one says a variable is uniform in a function?
Blum's paper is available at this link.
In this context, uniformity usually means that there exists an algorithm/Turing machine computing the thing that is being called uniform. That is, in this case, that there is a Turing machine that will compute $i,j$ from (Turing machines for) $f,g$.
More formally (in the context of the paper), it means:
There is a Turing machine $B$ such that, for any total Turing machines $F,G$, where $G$ has infinite range, $B(F,G)=(i,j)$ such that...