PFA and complemented subspaces of ℓ/c0

Alan Dow


The Banach space $\ell_\infty/c_0$ is isomorphic
to the linear space of continuous functions on $\mathbb N^*$ with the
supremum norm, $C(\mathbb N^*)$. Similarly, the canonical
representation of the
 $\ell_\infty$ sum of $\ell_\infty/c_0$ is the Banach space of
functions on the closure of any non-compact cozero subset of $\mathbb
N^*$.  It is important to determine if there is a continuous
linear lifting of this Banach space to a complemented
subset of $C(\mathbb N^*)$. We show that PFA implies there is no such

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Journal of Logic and Analysis ISSN:  1759-9008