# Arithmetical

• (adj): Relating to or involving arithmetic.
Example: "Arithmetical computations"
Synonyms: arithmetic

### Some articles on arithmetical:

Arithmetical Set - Properties
... The complement of an arithmetical set is an arithmetical set ... The Turing jump of an arithmetical set is an arithmetical set ... The collection of arithmetical sets is countable, but there is no arithmetically definable sequence that enumerates all arithmetical sets ...
Kleene's T Predicate - Arithmetical Hierarchy
... be used to generate complete sets in the arithmetical hierarchy ... This construction can be extended higher in the arithmetical hierarchy, as in Post's theorem (compare Hinman 2005, p ...
Definable Set - Examples - The Natural Numbers With Their Arithmetical Operations
... The sets definable in this structure are known as the arithmetical sets, and are classified in the arithmetical hierarchy ...
Reduction (recursion Theory) - Reductions Weaker Than Turing Reducibility
... They include Arithmetical reducibility A set A is arithmetical in a set B if A is definable over the standard model of Peano arithmetic with an extra predicate for B ... Equivalently, according to Post's theorem, A is arithmetical in B if and only if A is Turing reducible to, the nth Turing jump of B, for some natural number n ... The arithmetical hierarchy gives a finer classification of arithmetical reducibility ...
Implicitly Arithmetical Sets
... Each arithmetical set has an arithmetical formula which tells whether particular numbers are in the set ... whether the set itself satisfies some arithmetical property ... A set Y of natural numbers is implicitly arithmetical or implicitly arithmetically definable if it is definable with an arithmetical formula that is able to use Y as a parameter ...