Biorthogonal systems and quotient spaces via baire category methods

@article{Todorcevic2006BiorthogonalSA,
  title={Biorthogonal systems and quotient spaces via baire category methods},
  author={Stevo Todorcevic},
  journal={Mathematische Annalen},
  year={2006},
  volume={335},
  pages={687-715}
}
We show that every Banach space X of density smaller that the Baire category number admits a quotient with a long Schauder basis that can be taken of length ω1 if X is not separable. So, assuming that the Baire category number does not take its minimal possible value, a Banach space X is separable if and only if all biorthogonal systems of X are countable. 

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