A note on Tsirelson type ideals

Boban Veličković
1999 Fundamenta Mathematicae  
Using Tsirelson's well-known example of a Banach space which does not contain a copy of c 0 or lp, 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 fatcat:p4ehbejnonc2jfsrhy4gtsbnzu