… Finally, we consider to what extent our basis theorem can be strengthened. On the one
hand, a theorem of Solovay [15] gives (using measurable cardinals) a fl singleton, A c X, whose …

… For 1 < p < ∞ the only norm property that is not obvious is the Triangle Inequality, and this
can be shown by using exactly the same argument that we use later to prove Theorem 1.13. …

… The classical form of this result – the normal basis theorem – is that there exists an element
… a basis of E over F; α is a free element of E over F, and a basis like this is a normal basis over …

… We also prove that the analogous formal version of the Robson basis theorem is equivalent
to the … basis theorem is strictly and measurably greater than that of the Hilbert basis theorem. …

… “) is a F-Schauder basis. In this paper we prove a more general version of the theorem,
namely, a weak basis of closed subspaces in a Fréchet space is a Schauder basis of subspaces. …

… bers represented in the base y. A deeper theory is needed to treat conversion between bases
which are not variants of a common base, a condition which is specified for bases 13, v, by …

… , we seek theorems in our collection of established theorems with conclusions that …
theorem to establish the conclusion of the problem, because the truth of both the known theorem …

… Thus, Hilbert’s Basis Theorem can bc used to show that this … with the help of Griibner Base
methods, which thus prowdethe … Surprisingly, by construction of a Grobner Base algorithm for …

… the main theorem, from which we deduce the strong basis property and thus the basis
property. In Section 3, we prove that every inverse subsemigroup of Ix does indeed have a basis, …

… This generalization is very natural and does not complicate the proof of the basis theorem …
theorem. In the final section we discuss a criterion of Seidenberg related to the basis theorem. …