A note on Tsirelson type ideals

Tom 159 / 1999

Boban Veličković Fundamenta Mathematicae 159 (1999), 259-268 DOI: 10.4064/fm-159-3-259-268

Streszczenie

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.

Autorzy

  • Boban Veličković

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