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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 l p , for p ≥ 1, we construct a simple Borel ideal I T such that the Borel cardinalities of the quotient spaces P ( ) / I T and P ( ) / 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.

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