EFA is a very weak logical system, whose proof theoretic ordinal is
, but still seems able to prove much of ordinary mathematics that can be stated in the language of first-order arithmetic.
The axioms of EFA are Harvey Friedman's grand conjecture implies that many mathematical theorems, such as Fermat's Last Theorem, can be proved in very weak systems such as EFA.
Some natural examples include consistency statements from logic, several statements related to Ramsey theory such as the Szemerédi regularity lemma, and the graph minor theorem.
Several related computational complexity classes have similar properties to EFA: