# Enumerable Set

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Enumerable Set

the set of natural numbers or a set of other constructive objects that can be put into a one-to-one correspondence with the natural numbers. An enumerable set is definable by some general recursive function.

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Since v(r) is step function with r, so [mu](r) = [absolute value of [a.sub.v(r)]] [r.sup.v(r)] is differential everywhere except at an enumerable set of points of discontinuities of [absolute value of [a.sub.v(r)]] and v(r).
A sequential Martin-Lof test (briefly, M-L test) is a recursively enumerable set U [subset of equal to] N x [Q.sup.*] such that the level sets [U.sub.n] = {x [member of] [Q.sup.*] | (n, x) [member of] U} satisfy the following conditions:
A problem is considered to be partially decidable, semidecidable, solvable, or provable if A is a recursively enumerable set. Partially decidable problems and any other problems that are not decidable are referred to as undecidable.
When one or more of the physical parameters are modelled as random fields, it is essential, first, to represent them by an enumerable set of random variables.
He argues that the intuitively provable arithmetic sentences constitute a recursively enumerable set, which has a Godel sentence which is itself intuitively provable.
We prove that safe [Datalog.sup.??, [is less than]z]-programs do not have effective syntax in the sense that there is no recursively enumerable set S of safe [Datalog.sup.??, [is less than]z]-programs such that every safe [Datalog.sup.??, [is less than]z]-program is equivalent to a program in S.
Let an infinite, enumerable set of point particles [p.sub.i] (i [element of] {1, 2, 3, .
More precisely, [I.sub.n] (the phase) is defined on some enumerable set l; the sequence of phases (In) take values on state space I.
Since we may be reluctant (as are Nagel and Newman) to claim that 'the' human mind is capable of recognizing all arithmetic truths, this theorem does not in itself support Nagel and Newman However, it does lend some support because it can be proven as a consequence of the representability of any recursively enumerable set of strings S within any reasonable arithmetic axiomatization T.
Proposition 7 If F [[subset].bar] [summation over (term)] * is a computably enumerable set, then L[([X.sub.F]).sup.c]) is computably enumerable as well.
Solovay, "Recursively enumerable sets modulo iterated jumps and extensions of Arslanov's completeness criterion," The Journal of Symbolic Logic, vol.

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