Sentence examples for finite subset of from inspiring English sources

PA* is finitely consistent (i.e., every finite subset of PA* is consistent) hence consistent, hence by the Completeness Theorem it has a model.

Note that (E) is a finite subset of (G_0^mathrm{un}), and consequently that (G_0) is a finitely presented group.

Any finite subset of these sentences has a model.

A set Σ of sentences has a model [that is, an interpretation that makes it true] if any finite subset of Σ has a model.

In this paper, we define the concept of a spherical T-design for a finite subset of a sphere.

Let X be a nonempty finite subset of the sphere of dimension n−1, where n⩾3.

Since, in most applications, the number of propagating modes is a small finite subset of all the modes, the present condition yields a computationally efficient scheme.

LetLbe a finite subset of Euclideand-dimensional space Rdand letSbe a lattice in Rdsuch that {l−l′ : l, l′∈L}∩S={0}.

All of mathematics can be expressed in predicate logic, and Gödel showed that this logic has the following remarkable property: A set Σ of sentences has a model [that is, an interpretation that makes it true] if any finite subset of Σ has a model.

This suggests a stronger requirement on a formal system of logic namely, that p be derivable from X by the system whenever X logically entails p. The usual systems of logic satisfy this requirement because, besides the completeness theorem, there is also a compactness theorem: A theory X has a model if every finite subset of X has a model.

For any given nonempty finite subset of.