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Everything about Alpha recursion theory
Extension of recursion theory to admissible ordinals beyond the natural numbers
In recursion theory, Ī± recursion theory is a generalisation of recursion theory to subsets of admissible ordinals. An admissible set is closed under functions, where denotes a rank of Godel's constructible hierarchy. is an admissible ordinal if is a model of KripkeāPlatek set theory. In what follows is considered to be fixed. Wikipedia ā
š§ Start here: a 6-step reading path
- Read the overview: Alpha recursion theoryA 5-minute orientation
- Pick up a classic book: Contributions to axiomatic recursion theory and related aspects of alpha-recursion theoryThe most-reprinted book on the subject
- Read the landmark paper: Fragments of KripkeāPlatek set theory and the metamathematics of $$\alpha $$ Ī± -recursion theoryCited 7 times
- Go sideways: Large countable ordinalA closely related topic
- Go sideways: Admissible ordinalA closely related topic
š Definitions
No dictionary entry for this exact phrase.
šļø The subject at a glance
š Landmark papers (most cited)
š Books worth reading
- šContributions to axiomatic recursion theory and related aspects of alpha-recursion theoryJhu Ā· 1973
- šContributions to [alpha]- and [beta]-recursion theoryMaass, Wolfgang Ā· 1978
Introduction to making very big booksUnited States. Congress. Senate. Committee on Pensions Ā· 2011
Selected papers on analysis of algorithmsDonald Knuth Ā· 2000
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
š Related topics
- Large countable ordinal In the mathematical discipline of set theory, there are many ways of describing specific countable ordinals. The smallest ones can be usefully and non-circularlā¦
- Admissible ordinal In set theory, an ordinal number Ī± is an admissible ordinal if LĪ± is an admissible set (that is, a transitive model of KripkeāPlatek set theory); in otherā¦
- Constructible universe In set theory, the constructible universe (or Gƶdel's constructible universe), denoted by L, is a particular class of sets that can be described entirelyā¦
- Ordinal analysis In proof theory, ordinal analysis assigns ordinals (often large countable ordinals) to mathematical theories as a measure of their strength. If theoriesā¦
- Computability theory Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originatedā¦
- Computably enumerable set In computability theory, a set S of natural numbers is called computably enumerable (c.e.), recursively enumerable (r.e.), semidecidable, partially decidableā¦
- KripkeāPlatek set theory KripkeāPlatek set theory (KP) is an axiomatic set theory developed by Saul Kripke and Richard Platek. It is substantially weaker than ZermeloāFraenkelā¦
- Kleene's recursion theorem In computability theory, Kleene's recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptionsā¦