I'm not sure, whether there is a commonly used and sort of outstanding one. If there was such, it would be incredibly easy to google. Or at least all Analysis books would've been mentioning that the subject is based on this particular formal first-order theory that everyone uses.
2026-04-04 15:08:26.1775315306
Which formal theory is commonly used to describe mathematical analysis?
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All of analysis can be developed within $\mathsf{ZFC}$ set-theory, as can almost all of modern mathematics.This isn’t mentioned in most analysis books, because most analysts probably don’t care too much about foundations, and they’d probably accept any foundation that lets them make their arguments.