#### History of the paper

###### 2006

The paper was written at UConn.

###### 2009

Paper appeared in print:

Finding paths through narrow and wide trees

(with Stephen E. Binns). Journal of Symbolic Logic **74** (2009), no. 1, 349—360.

###### 2012

Laurent Bienvenu and Paul Shafer discovered an apparent error in the proof of Lemma 4.6. There it is stated that A wtt-reduces to B; however, it seems that the reduction of A to B also requires oracle access to f. Corollary 4.7 also seems false (take f to be a ML random of hyperimmune-free degree, and A=f; then A is complex but not f-complex).