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Computability theory and Hyperarithmetical theory

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Computability theory and Hyperarithmetical theory

Computability theory vs. Hyperarithmetical theory

Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. In recursion theory, hyperarithmetic theory is a generalization of Turing computability.

Similarities between Computability theory and Hyperarithmetical theory

Computability theory and Hyperarithmetical theory have 14 things in common (in Unionpedia): Alpha recursion theory, Analytical hierarchy, Arithmetical hierarchy, Computable function, Effective descriptive set theory, Many-one reduction, Natural number, Peano axioms, Second-order arithmetic, Set theory, Tarski's undefinability theorem, Turing degree, Turing jump, Turing reduction.

Alpha recursion theory

In recursion theory, α recursion theory is a generalisation of recursion theory to subsets of admissible ordinals \alpha.

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Analytical hierarchy

In mathematical logic and descriptive set theory, the analytical hierarchy is an extension of the arithmetical hierarchy.

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Arithmetical hierarchy

In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy classifies certain sets based on the complexity of formulas that define them.

Arithmetical hierarchy and Computability theory · Arithmetical hierarchy and Hyperarithmetical theory · See more »

Computable function

Computable functions are the basic objects of study in computability theory.

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Effective descriptive set theory

Effective descriptive set theory is the branch of descriptive set theory dealing with sets of reals having lightface definitions; that is, definitions that do not require an arbitrary real parameter (Moschovakis 1980).

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Many-one reduction

In computability theory and computational complexity theory, a many-one reduction is a reduction which converts instances of one decision problem into instances of a second decision problem.

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Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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Peano axioms

In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.

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Second-order arithmetic

In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets.

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Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

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Tarski's undefinability theorem

Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1936, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics.

Computability theory and Tarski's undefinability theorem · Hyperarithmetical theory and Tarski's undefinability theorem · See more »

Turing degree

In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures the level of algorithmic unsolvability of the set.

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Turing jump

In computability theory, the Turing jump or Turing jump operator, named for Alan Turing, is an operation that assigns to each decision problem a successively harder decision problem with the property that is not decidable by an oracle machine with an oracle for.

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Turing reduction

In computability theory, a Turing reduction from a problem A to a problem B, is a reduction which solves A, assuming the solution to B is already known (Rogers 1967, Soare 1987).

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The list above answers the following questions

Computability theory and Hyperarithmetical theory Comparison

Computability theory has 101 relations, while Hyperarithmetical theory has 25. As they have in common 14, the Jaccard index is 11.11% = 14 / (101 + 25).

References

This article shows the relationship between Computability theory and Hyperarithmetical theory. To access each article from which the information was extracted, please visit:

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