Alpha recursion theory

<p>In <a href="/facts/Recursion_theory/cqDfXwdf">recursion theory</a>, α recursion theory is a generalisation of <a href="/facts/Recursion_theory/cqDfXwdf">recursion theory</a> to subsets of <a href="/facts/Admissible_ordinal/2uKMaeAP">admissible ordinals</a> 
  
    
      
        α
      
    
    {\displaystyle \alpha }
  
.  An admissible set is closed under 
  
    
      
        
          Σ
          
            1
          
        
        (
        
          L
          
            α
          
        
        )
      
    
    {\displaystyle \Sigma _{1}(L_{\alpha })}
  
 functions, where 
  
    
      
        
          L
          
            ξ
          
        
      
    
    {\displaystyle L_{\xi }}
  
 denotes a rank of Godel's <a href="/facts/Constructible_hierarchy/pxU0cmL3">constructible hierarchy</a>. 
  
    
      
        α
      
    
    {\displaystyle \alpha }
  
 is an admissible ordinal if 
  
    
      
        
          L
          
            α
          
        
      
    
    {\displaystyle L_{\alpha }}
  
 is a  model of <a href="/facts/Kripke%25E2%2580%2593Platek_set_theory/nrA8tqBB">Kripke–Platek set theory</a>.  In what follows 
  
    
      
        α
      
    
    {\displaystyle \alpha }
  
 is considered to be fixed.
</p>

Alpha recursion theory open-in-new

Alpha recursion theory