Aug. 30 2008
I thank Anthony Quas and Mahsa Allahbakhshi
for pointing out to me an error in my paper
"Putnam's resolving maps in dimension zero".
There I defined the "resolving degree" of a block code
from an irreducible SFT to a possibly sofic shift.
For a finite to one code, this is the usual degree.
The error:
Proposition 7.1 claims that the resolving degree
is an invariant of topological conjugacy for factor
maps from irreducible shifts of finite type to
sofic systems, even in the case that the factor maps
are infinite to one. This is not true.
As pointed out by Anthony and Mahsa, if the factor
map collapses the domain to a single point, then the
resolving degree is simply the cardinality of the
domain alphabet. Obviously this is not invariant
under conjugacy when the domain has positive entropy.
The (uninteresting) error in the proof is the phrase
"and the cardinality of its preimage, which is the
degree of p_2, is the cardinality of pi^{-1}(mu)."
This is a claim that the number of symbols p_2 maps
to the symbol {mu} is equal to the number of symbols
pi maps to the symbol mu.
I believe the error has no implication for the correctness
of the rest of the paper. Where resolving degree and magic
words are used for infinite to one maps, there is no
use of invariance under topological conjugacy.
============================
There is also a possibly confusing typo on p.1496 in the
first line of the proof of Theorem 5.4. There,
$\mathcal D(\pi )$ should be $\mathcal D^{(1)}(\pi )$.