Aligning labels at the side of tikz diagram

Question

I'm using the tikz package to create diagrams showing the formation process of simple fractals, the first one being is the Cantor set. I'm showing a couple of iterations each one below the previous with its corresponding label at the side and then a larger space before the final fractal set, along with some vertical dots between the label. This is my current code

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}

\begin{document}
\usetikzlibrary{decorations.fractals}


\begin{tikzpicture}[xscale = 3.0, yscale=1, decoration=Cantor set,very thick] 
\draw decorate{ (0,0) -- (3,0) };
\node at (3,0) [right] {$E_0$};
\node at (3,-1) [right] {$E_1$};
\node at (3,-2) [right] {$E_2$};
\node at (3,-3) [right] {$\vdots$};
\node at (3,-4) [right] {$F$};
\draw decorate{ decorate{ (0,-1) -- (3,-1) }};
\draw decorate{ decorate{ decorate{ (0,-2) -- (3,-2) }}};
\draw decorate{ decorate{ decorate{ decorate{ decorate{ decorate{ decorate{(0,-4) -- (3,-4) }}}}}}};
\end{tikzpicture}
\end{document}

My issue is that I'm unsure of how to make it so that the labels are aligned. An ideal answer would be one that would require minimal changes when applied fractal figures where the vertical spacing will be different. Thanks in advance!

Answer 1

since question is not clear (to me), let helps us with following picture:

is this, what you looking for?

\documentclass[tikz, margin=3mm]{standalone}
\usepgflibrary{decorations.fractals}

\begin{document}
\begin{tikzpicture}[xscale = 3.0, yscale=1, decoration=Cantor set,very thick]
\draw decorate{(0,0) -- (3,0)} node[right] {$E_0$};
\draw decorate{ decorate{ (0,-1) -- (3,-1) }} node [right] {$E_1$};
\draw decorate{ decorate{ decorate{ (0,-2) -- (3,-2) }}} node[right] (e2) {$E_2$};
\draw decorate{ decorate{ decorate{ decorate{ decorate{ decorate{ decorate{(0,-4) -- (3,-4) }}}}}}} node [right] (f) {$F$};
\node at ($(e2)!0.5!(f)$) {$\vdots$};
\end{tikzpicture}

\end{document}