There is an extensive recursive set of path constructors available.

Let be a class (called a simple game and thought of as a property) of recursive sets.

A string is winning determining if any recursive set extending belongs to .

In computability theory, an undecidable problem is a problem whose language is not a recursive set.

A decision problem A is called decidable or effectively solvable if A is a recursive set.

In this section, we give an analogue of Rice's theorem for recursive sets, instead of recursively enumerable sets.

Hereditary Harrop formulae are defined in terms of two (sometimes three) recursive sets of formulae.

If A is a recursive set then the complement of A is a recursive set.

The preimage of a recursive set under a total computable function is a recursive set.

A set A is a recursive set if and only if A and the complement of A are both recursively enumerable sets.

In computability theory, recursively inseparable sets are pairs of sets of natural numbers that cannot be "separated" with a recursive set (Monk 1976, p. 100).

Beginning with the theory of recursive sets and functions described above, the field of recursion theory has grown to include the study of many closely related topics.

EXAMPLE: Each infinite RE set contains an infinite recursive set.

If L is finitely axiomatizable (and has a recursive set of recursive rules) and has the fmp, then it is decidable.

The proof above shows that for each recursively enumerable set of axioms there is a recursive set of axioms with the same deductive closure.

Every recursive set is recursively enumerable, but it is not true that every recursively enumerable set is recursive.

According to Tarski's account, meaning consists of a recursive set of rules that end up yielding an infinite set of sentences, "'p' is true if and only if p", covering the whole language.

This article is a temporary experiment to see whether it is feasible and desirable to merge the articles Recursive set, Recursive language, Decidable language, Decidable problem and Undecidable problem.

Roughly speaking, the analogue says that if one can effectively determine for any recursive set whether it has a certain property, then finitely many integers determine whether a recursive set has the property.

John McCarthy posed a puzzle to him about spies, guards, and password which Rabin studied and soon after he wrote an article, "Degree of Difficulty of Computing a Function and Hierarchy of Recursive Sets."

If A and B are recursive sets then A B, A B and the image of A x B under the Cantor pairing function are recursive sets.

Post's original motivation in the study of this lattice was to find a structural notion such that every set which satisfies this property is neither in the Turing degree of the recursive sets nor in the Turing degree of the halting problem.

These models enable some nonrecursive sets of numbers or languages (including all recursively enumerable sets of languages) to be "learned in the limit"; whereas, by definition, only recursive sets of numbers or languages could be identified by a Turing machine.

A class of recursive sets is computable if and only if there are a recursively enumerable set of losing determining strings and a recursively enumerable set of winning determining strings such that any recursive set extends a string in .