What is the meaning of $\Sigma_n, \Pi_n, \Delta_n$ without superscript symbols?

Question

Sometimes I see the $\Sigma_n, \Pi_n, \Delta_n$ notation without superscript symbols (for example, in this answer on Mathoverflow; another example is hypermachines ($\Sigma_n$-machines)). But when I read articles on Wikipedia (Descriptive set theory, Arithmetical hierarchy, Hyperarithmetical theory, Analytical hierarchy, Projective hierarchy, Borel hierarchy), I only see the notation with superscript symbols, and I cannot find what is implied by $\Sigma_n, \Pi_n, \Delta_n$. Why is the superscript symbol omitted?

Answer 1

This notation implies a formula in the Lévy hierarchy.