Elementary Functional Arithmetic

Elementary Functional Arithmetic, or EFA, is a weak theory of arithmeticPlanetmathPlanetmath created by removing inductionMathworldPlanetmath from Peano ArithmeticMathworldPlanetmathPlanetmath. Because it lacks induction, axioms defining exponentiationPlanetmathPlanetmath must be added.

  • x(x0) (0 is the first number)

  • x,y(x=yx=y) (the successor function is one-to-one)

  • x(x+0=x) (0 is the additive identity)

  • x,y(x+y=(x+y)) (addition is the repeated application of the successor function)

  • x(x0=0)

  • x,y(x(y)=xy+x (multiplication is repeated addition)

  • x(¬(x<0)) (0 is the smallest number)

  • x,y(x<yx<yx=y)

  • x(x0=1)

  • x(xy=xyx)

Title Elementary Functional Arithmetic
Canonical name ElementaryFunctionalArithmetic
Date of creation 2013-03-22 12:56:39
Last modified on 2013-03-22 12:56:39
Owner Henry (455)
Last modified by Henry (455)
Numerical id 5
Author Henry (455)
Entry type Definition
Classification msc 03F30
Synonym EFA
Related topic PeanoArithmetic