# A note on Tsirelson type ideals

Fundamenta Mathematicae (1999)

- Volume: 159, Issue: 3, page 259-268
- ISSN: 0016-2736

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topVeličković, Boban. "A note on Tsirelson type ideals." Fundamenta Mathematicae 159.3 (1999): 259-268. <http://eudml.org/doc/212333>.

@article{Veličković1999,

abstract = {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.},

author = {Veličković, Boban},

journal = {Fundamenta Mathematicae},

keywords = {trichotomy conjecture; dichotomy conjecture; Borel equivalence relations; Polish space; Tsirelson's Banach space; Borel ideal; Borel cardinalities; quotient spaces},

language = {eng},

number = {3},

pages = {259-268},

title = {A note on Tsirelson type ideals},

url = {http://eudml.org/doc/212333},

volume = {159},

year = {1999},

}

TY - JOUR

AU - Veličković, Boban

TI - A note on Tsirelson type ideals

JO - Fundamenta Mathematicae

PY - 1999

VL - 159

IS - 3

SP - 259

EP - 268

AB - 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.

LA - eng

KW - trichotomy conjecture; dichotomy conjecture; Borel equivalence relations; Polish space; Tsirelson's Banach space; Borel ideal; Borel cardinalities; quotient spaces

UR - http://eudml.org/doc/212333

ER -

## References

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