منابع مشابه
On the Hamkins approximation property
We give a short proof of a lemma which generalizes both the main lemma from the original construction in the author’s thesis of a model with no ω2-Aronszajn trees, and also the “Key Lemma” in Hamkins’s gap forcing theorems. The new lemma directly yields Hamkins’s newer lemma stating that certain forcing notions have the approximation property. According to Hamkins [2], a partial ordering P sati...
متن کاملHamkins on the Multiverse
Ever since the rise of non-standard models and the proliferation of the independence results there have been two conflicting positions in the foundations of mathematics. The first position—which we shall call pluralism—maintains that certain statements of mathematics do not have determinate truth-values. On this view, although it is admitted that there are are practical reasons that one might g...
متن کاملThe Strong Approximation Property and the Weak Bounded Approximation Property
We show that the strong approximation property (strong AP) (respectively, strong CAP) and the weak bounded approximation property (respectively, weak BCAP) are equivalent for every Banach space. This gives a negative answer to Oja’s conjecture. As a consequence, we show that each of the spaces c0 and `1 has a subspace which has the AP but fails to have the strong AP.
متن کاملHereditary Approximation Property
If X is a Banach space such that the isomorphism constant to `2 from n dimensional subspaces grows sufficiently slowly as n → ∞, then X has the approximation property. A consequence of this is that there is a Banach space X with a symmetric basis but not isomorphic to `2 so that all subspaces of X have the approximation property. This answers a problem raised in 1980 [8]. An application of the ...
متن کاملA note on interpolation, best approximation, and the saturation property
In this note, we prove that the well known saturation assumption implies that piecewise polynomial interpolation and best approximation in finite element spaces behave in similar fashion. That is, the error in one can be used to estimate the error in the other. We further show that interpolation error can be used as an a posteriori error estimate that is both reliable and efficient.
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2006
ISSN: 0168-0072
DOI: 10.1016/j.apal.2006.05.005