# On a conjecture of Dobrinen and Simpson concerning almost everywhere domination

On a conjecture of Dobrinen and Simpson concerning almost everywhere domination (with Stephen Binns, Manuel Lerman, and Reed Solomon). Journal of Symbolic Logic 71 (2006), no. 1, 119—136.

This paper was concerned with the difference between highness and almost everywhere domination in the Turing degrees. This was taken further in later papers.

# Lowness for the class of Schnorr random reals

Lowness for the class of Schnorr random reals (with André Nies and Frank Stephan).SIAM Journal on Computing 35 (2005), no. 3, 647—657 (electronic).

In this paper the idea of mixed lowness notions seems to have been born (?). This idea actually occurred to me while unlocking my bicycle in Heidelberg.

# Comparing DNR and WWKL

Comparing DNR and WWKL (with Klaus Ambos-Spies, Steffen Lempp, and Theodore A. Slaman).
Journal of Symbolic Logic
69 (2004), no. 4, 1089—1104.

This paper (which is mentioned in Wikipedia under Reverse Mathematics) separated DNR from WWKL. It was mostly written while all four authors were in Heidelberg during 2002-2003.

# Local initial segments of the Turing degrees

Local initial segments of the Turing degrees
Bulletin of Symbolic Logic
9 (2003), no. 1, 26—36.

This paper described the results of my doctoral dissertation “Lattice initial segments of the Turing degrees”.