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 $\mathcal D^{(1)}(\pi )$.