Elementary function arithmetic

<p>In <a href="/facts/Proof_theory/kopBdQn9">proof theory</a>, a branch of <a href="/facts/Mathematical_logic/SaI7Y3wN">mathematical logic</a>, 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, +, ×, 
  
    
      
        
          x
          
            y
          
        
      
    
    {\displaystyle x^{y}}
  
, together with <a href="/facts/Mathematical_induction/KxAPqNrH">induction</a> for  formulas with <a href="/facts/Bounded_quantifier/Q0Y7aTkG">bounded quantifiers</a>.
</p><p>EFA is a very weak logical system, whose <a href="/facts/Proof_theoretic_ordinal/bx5joaVU">proof theoretic ordinal</a> is 
  
    
      
        
          ω
          
            3
          
        
      
    
    {\displaystyle \omega ^{3}}
  
, but still seems able to prove much of ordinary mathematics that can be stated in the language of <a href="/facts/Peano_axioms/DhhDnNug">first-order arithmetic</a>.
</p>

Elementary function arithmetic open-in-new

Elementary function arithmetic