Elementary function arithmetic

In proof theory, a branch of mathematical logic, elementary function arithmetic (EFA), also called elementary arithmetic and exponential function arithmetic, is the system of arithmetic with the usual elementary properties of 0, 1, +, ×, 

EFA is a system in first-order logic (with equality). Its language contains:

• two constants +, exp(x,y) usually written as ∀(x<y) and ∃x(x<y)∧… in the usual way.

  The axioms of EFA are

  • The axioms of Robinson arithmetic for +, x0=1,

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