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 
@article{10_4064_fm_159_3_259_268,
     author = {Boban Veli\v{c}kovi\'c},
     title = {A note on {Tsirelson} type ideals},
     journal = {Fundamenta Mathematicae},
     pages = {259--268},
     publisher = {mathdoc},
     volume = {159},
     number = {3},
     year = {1999},
     doi = {10.4064/fm-159-3-259-268},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-159-3-259-268/}
}
TY  - JOUR
AU  - Boban Veličković
TI  - A note on Tsirelson type ideals
JO  - Fundamenta Mathematicae
PY  - 1999
SP  - 259
EP  - 268
VL  - 159
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm-159-3-259-268/
DO  - 10.4064/fm-159-3-259-268
LA  - en
ID  - 10_4064_fm_159_3_259_268
ER  - 
%0 Journal Article
%A Boban Veličković
%T A note on Tsirelson type ideals
%J Fundamenta Mathematicae
%D 1999
%P 259-268
%V 159
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm-159-3-259-268/
%R 10.4064/fm-159-3-259-268
%G en
%F 10_4064_fm_159_3_259_268
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

Cité par Sources :