Godel Numbering and Parenthes

Question

I am teaching myself more about mathematical logic. I do not know if parenthesis get included in Godel numbering. In the Translated Original Presburger Arithmetic Paper he makes the claim that "the meaningful statements are all built with:" (p. 8 of 21) and doesn't include parenthesis. Yet, when I looked up the Godel numbering for Peano axioms on Wikipedia, they include parenthesis. And in the original paper he calls the statement $\exists\alpha(\alpha+1=0)$ meaningful (p. 10 of 21). Is there a way to write every formula in Presburger arithmetic without parenthesis?

Answer 1

You can use prefix notation, e.g. look up 'Polish notation'

E.g. your claim would be something like

$\exists \alpha = + \alpha 1 0$