A note on Tsirelson type ideals

  title={A note on Tsirelson type ideals},
  author={Boban and Paris},
  • Boban, Paris
  • Published 2007
Using Tsirelson’s well-known example of a Banach space which does not contain a copy of c0 or lp, for p ≥ 1, we construct a simple Borel ideal IT such that the Borel cardinalities of the quotient spaces P(N)/IT and P(N)/I0 are incomparable, where I0 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. Introduction. Given Borel equivalence relations E and F on Polish spaces X and Y… CONTINUE READING