Post's Theorem relates the levels of the arithmetical hierarchy, which classifies sets of natural numbers by the logical complexity of the formulas that define them, to the Turing jump operation, showing that the sets definable at one level correspond exactly to the sets computable relative to the Turing jump of the oracle characterizing the level below. Named for Emil Post, it is a foundational result of computability theory connecting definability and relative computability.
Facts
StatementPost's theorem describes the connection between the arithmetical hierarchy and the Turing degrees. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Source Post's theorem, Wikipedia
Proved By
Source Post's theorem, Wikipedia
Sources
1. Post's theorem, Wikipedia
Lead, first sentence
In computability theory, Post's theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees.
In Branch: Computability Theory, Lead sentence
In computability theory, Post's theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and th
Proved By: Emil Post, Lead paragraph
In computability theory, Post's theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees.
In Group: Computability and Complexity Theory, Lead section
In computability theory, Post's theorem, named after Emil Post, describes
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.