In computability theory a numbering is the assignment of natural numbers to a set of objects such as functions, rational numbers, graphs, or words in some...

Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated...

Computability is the ability to solve a problem by an effective procedure. It is a key topic of the field of computability theory within mathematical...

whose table definitions require a database design. In computability theory, the simplest numbering scheme is the assignment of natural numbers to a set...

Recursive Functions and Effective Computability, MIT Press. ISBN 0-262-68052-1 S. Barry Cooper (2004). Computability Theory. Chapman and Hall/CRC. ISBN 1-58488-237-9...

Stoltenberg-Hansen, V.; Tucker, J.V. (1999). "Computable Rings and Fields". In Griffor, E.R. (ed.). Handbook of Computability Theory. Elsevier. pp. 363–448. ISBN 978-0-08-053304-9...

In computability theory, a set of natural numbers is computable (or decidable or recursive) if there is an algorithm that computes the membership of every...

Computable functions are the basic objects of study in computability theory. Informally, a function is computable if there is an algorithm that computes...

and completeness properties of formal systems. In computability theory, the term "Gödel numbering" is used in settings more general than the one described...

In computability theory, a set S of natural numbers is called computably enumerable (c.e.), recursively enumerable (r.e.), semidecidable, partially decidable...

In computability theory, admissible numberings are enumerations (numberings) of the set of partial computable functions that can be converted to and from...

In computability theory, many reducibility relations (also called reductions, reducibilities, and notions of reducibility) are studied. They are motivated...

Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers...

In computability theory, the Church–Turing thesis (also known as computability thesis, the Turing–Church thesis, the Church–Turing conjecture, Church's...

analysis of algorithms and computability theory. A key distinction between analysis of algorithms and computational complexity theory is that the former is...

contradiction. The logic involved is closer to proof theory than to that of computability theory and computable functions. It is rather loosely conjectured that...

In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question on a...

In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all...

In computational complexity theory and computability theory, a counting problem is a type of computational problem. If R is a search problem then c R...

Computable model theory is a branch of model theory which deals with questions of computability as they apply to model-theoretical structures. Computable...

In computability theory, index sets describe classes of computable functions; specifically, they give all indices of functions in a certain class, according...

in this theory, the existence of a surjection from I onto S need not imply the existence of an injection from S into I. In computability theory one often...

In computability theory two sets A , B {\displaystyle A,B} of natural numbers are computably isomorphic or recursively isomorphic if there exists a total...

In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct...

Computability logic (CoL) is a research program and mathematical framework for redeveloping logic as a systematic formal theory of computability, as opposed...

machines has yielded many insights into computer science, computability theory, and complexity theory. In his 1948 essay, "Intelligent Machinery", Turing wrote...

Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic...

In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the...

In computability theory, two disjoint sets of natural numbers are called computably inseparable or recursively inseparable if they cannot be "separated"...

In computability theory, Kleene's recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions...