TikZ graphic for arithmetic hierarchy

ArithmeticHierarchy.tex

\documentclass{standalone}
\usepackage{amsmath}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[node distance=2cm,semithick,-latex]
\node(1){$\Delta_1^0$};
\node(1a)[above right of=1]{$\Sigma_1^0$};
\node(1b)[below right of=1]{$\Pi_1^0$};
\node(2)[above right of=1b]{$\Delta_2^0$};
\path (1) edge (1a);
\path (1) edge (1b);
\path (1a) edge (2);
\path (1b) edge (2);


\node(2a)[above right of=2]{$\Sigma_2^0$};
\node(2b)[below right of=2]{$\Pi_2^0$};
\node(3)[above right of = 2b]{};
\path (2) edge (2a);
\path (2) edge (2b);
\path (2a) edge (3);
\path (2b) edge (3);

\node(3)[right of = 3,node distance=0.5cm]{$\ldots$};
\node [above of=3,node distance = 1cm]{$\ldots$};
\node [below of=3,node distance = 1cm]{$\ldots$};

\node(3)[right of = 3, node distance = 0.7cm]{$\Delta_\alpha^0$};

\node(3a)[above right of=3]{$\Sigma_\alpha^0$};
\node(3b)[below right of=3]{$\Pi_\alpha^0$};
\node(4)[below right of=3a]{$\quad\Delta_{\alpha+1}^0$};
\path (3) edge (3a);
\path (3) edge (3b);
\path (3a) edge (4);
\path (3b) edge (4);

\node (5) [right of=4,node distance = 1cm]{$\ldots$};
\node (5a) [above of=5,node distance = 1cm]{$\ldots$};
\node (5b) [below of=5,node distance = 1cm]{$\ldots$};
\end{tikzpicture}

\end{document}