A note on Tsirelson type ideals

Veličković, Boban

Fundamenta Mathematicae, Tome 159 (1999), p. 259-268 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $\sum_{n \in A} 1 / (n + 1) < \infty$ . This disproves a “trichotomy” conjecture for Borel ideals proposed by Kechris and Mazur.

Publié le : 1999-01-01

Zbl 0930.03056

EUDML-ID : urn:eudml:doc:212333

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     author = {Boban Veli\v ckovi\'c},
     title = {A note on Tsirelson type ideals},
     journal = {Fundamenta Mathematicae},
     volume = {159},
     year = {1999},
     pages = {259-268},
     zbl = {0930.03056},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv159i3p259bwm}
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Veličković, Boban. A note on Tsirelson type ideals. Fundamenta Mathematicae, Tome 159 (1999) pp. 259-268. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv159i3p259bwm/

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