Elementary function arithmetic: Difference between revisions

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{{No footnotes|date=November 2017}}

In [[proof theory]], a branch of [[mathematical logic]], '''elementary function arithmetic''', also called ('''EFA'''), also called '''elementary arithmetic''' and '''exponential function arithmetic''', is the system of arithmetic with the usual elementary properties of 0, 1, +, ×, ''x''^''y'', together with [[mathematical induction|induction]] for formulas with [[bounded quantifier]]s.

EFA is a very weak logical system, whose [[proof theoretic ordinal]] is ω³, but still seems able to prove much of ordinary mathematics that can be stated in the language of [[Peano axioms|first-order arithmetic]].