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- Alpha_recursion_theory abstract "In recursion theory, α recursion theory is a generalisation of recursion theory to subsets of admissible ordinals . An admissible ordinal is closed under functions. Admissible ordinals are models of Kripke–Platek set theory. In what follows is considered to be fixed.The objects of study in recursion are subsets of . A is said to be recursively enumerable if it is definable over . A is recursive if both A and (its complement in ) are recursively enumerable.Members of are called finite and play a similar role to the finite numbers in classical recursion theory.We say R is a reduction procedure if it is recursively enumerable and every member of R is of the form where H, J, K are all α-finite.A is said to be α-recusive in B if there exist reduction procedures such that: If A is recursive in B this is written . By this definition A is recursive in (the empty set) if and only if A is recursive. However A being recursive in B is not equivalent to A being .We say A is regular if or in other words if every initial portion of A is α-finite.".
- Alpha_recursion_theory wikiPageID "12008116".
- Alpha_recursion_theory wikiPageRevisionID "476025276".
- Alpha_recursion_theory hasPhotoCollection Alpha_recursion_theory.
- Alpha_recursion_theory subject Category:Computability_theory.
- Alpha_recursion_theory comment "In recursion theory, α recursion theory is a generalisation of recursion theory to subsets of admissible ordinals . An admissible ordinal is closed under functions. Admissible ordinals are models of Kripke–Platek set theory. In what follows is considered to be fixed.The objects of study in recursion are subsets of . A is said to be recursively enumerable if it is definable over .".
- Alpha_recursion_theory label "Alpha recursion theory".
- Alpha_recursion_theory sameAs m.02vls68.
- Alpha_recursion_theory sameAs Q4735170.
- Alpha_recursion_theory sameAs Q4735170.
- Alpha_recursion_theory wasDerivedFrom Alpha_recursion_theory?oldid=476025276.
- Alpha_recursion_theory isPrimaryTopicOf Alpha_recursion_theory.