How to pronounce $\Sigma_1$?

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I have to give a presentation and part of it involves talking about the recursively enumerable sets. However, some of the theorems I am quoting (like Rosser's proof of Godel's first incompleteness theorem) write $\Sigma_1$-sets instead.

Do I literally pronounce this "Sigma 1 sets"? Thank you.

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The ones with only a subscript are pronounced as they look:

  • $\Sigma_1$ : "sigma one"
  • $\Pi_n$ : "pi en"

When there is a numerical subscript and a numerical superscript, pronounce the superscript first.

  • $\Sigma^0_1$ : "sigma zero one"

  • $\Pi^1_2$ : "pi one two"

  • $\Pi^n_1$ : "pi en one"

  • $\Sigma^0_n$ : "sigma zero en"

When the superscript is a set, the pronunciation is more complicated. For example $\Sigma_1^A$ could mean the collection of sets that are $\Sigma_1$ relative to a set $A$. This might be pronounced "sigma 1 in A".

Similarly, $\Sigma^\text{ZF}_1$ might be pronounced "sigma 1 in Z F", "sigma 1 in the language of ZF", or some other way (in general $\Sigma^T_n$ for $T$ a theory is the class of formulas that are provably equivalent in $T$ to a $\Sigma_n$ formula) and, if $C$ is a complexity class, $\Sigma^C_n$ would be "Sigma n C", the $\Sigma_n$ level of the $C$-hierarchy.