I am trying to make sense of the following, in Proposition 1.5 of this paper.
Let $E$ be the exterior algebra over $\mathbb{F}_2$ with a generator $x_i\in E_{2^i}$ for all $i\in\mathbb{N}$.
I understand the definition on Wikipedia here of the exterior algebra of a vector space $V$ over a field $K$, and therefore of the exterior algebra of a vector space over $\mathbb{F}_2$. But how does this relate to $E$ above? So far as I can tell, $E_n$ is not defined anywhere, so I cannot make sense of $E_{2^i}$ either.
How can I understand exactly what $E$ is?
Also, just before this, there is a reference to 'the exterior algebra $$\mathbb{F}_2[x_0,\ldots,x_n]/(x_0^2,\ldots,x_n^2).$$
What $\mathbb{F}_2$-vector space is this the exterior algebra of? I think I have completely misunderstood this.