Errata for "Constructions with Countable Subshifts of Finite Type"
There is a mistake in the proof of Proposition 5.7. The case where w occurs infinitely many times on a finite set of rows is missed. This turns out to lead to a bunch of complications, and indeed we do not know whether the result of true, though it can be proved under some additional assumptions on the subshift.
In the paper, the purpose of the proposition is to yield Corollary 5.8 and Corollary 5.9 (which deal with the P property directly). These corollaries are given direct proofs in the PhD thesis of the second-named author. It remains an interesting question what kind of relations exist between the CB-rank of a subshift and the CB-rank of its projective subdynamics.
Last update: 9.8.2017