Geodesic
A note on Tsirelson type ideals
Fundamenta Mathematicae, Tome 159 (1999) no. 3, pp. 259-268.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Using Tsirelson's well-known example of a Banach space which does not contain a copy of $c_0$ or $l_p$, for p ≥ 1, we construct a simple Borel ideal $I_T$ such that the Borel cardinalities of the quotient spaces $P(ℕ)/I_T$ and $P(ℕ)/I_0$ are incomparable, where $I_0$ is the summable ideal of all sets A ⊆ ℕ such that $∑ _{n ∈ A}1/(n+1) ∞$. This disproves a "trichotomy'' conjecture for Borel ideals proposed by Kechris and Mazur.
DOI : 10.4064/fm-159-3-259-268

Boban Veličković 1

1 
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Boban Veličković. A note on Tsirelson type ideals. Fundamenta Mathematicae, Tome 159 (1999) no. 3, pp. 259-268. doi : 10.4064/fm-159-3-259-268. http://geodesic.mathdoc.fr/articles/10.4064/fm-159-3-259-268/

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