### 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 -

... be used to generate complete sets in the

**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

... The sets definable in this structure are known as the

**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

... 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

... Each

**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 ...Main Site Subjects

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