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In proof theory, a branch of mathematical logic, elementary function arithmetic , also called elementary arithmetic and exponential function arithmetic, is the system of arithmetic with the usual elementary properties of 0, 1, +, ×, x, together with induction for formulas with bounded quantifiers.
EFA is a very weak logical system, whose proof theoretic ordinal is ω, but still seems able to prove much of ordinary mathematics that can be stated in the language of first-order arithmetic.
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