analytical hierarchy and individual variable quantifiers

Question

For analytical hierarchy, $\Sigma^1_0$ is usually defined as the class of formula that does not have any set quantifier - but does this mean that there can be any number of quantifiers for individual variable?

Answer 1

Yes, $\Sigma^1_0$ and $\Pi^1_0$ formulas are exactly the arithmetical formulas, which can also be denoted $\Sigma^0_\infty$ and $\Pi^0_\infty$. They can have any number of number quantifiers.