Page "Reverse mathematics" Paragraph 3

In reverse mathematics, one starts with a framework language and a base theory — a core axiom system — that is too weak to prove most of the theorems one might be interested in, but still powerful enough to develop the definitions necessary to state these theorems.

For example, to study the theorem “ Every bounded sequence of real numbers has a supremum ” it is necessary to use a base system which can speak of real numbers and sequences of real numbers.