The degrees of unsolvability: the ordering of functions by relative computability; in Proceedings of the International Congress of Mathematicians (Warsaw) 1983, PWN-Polish Scientific Publishers, Warsaw 1984, Vol. 1, 337–346.
Logic for Applications (with A. Nerode), Texts and Monographs in Computer Science, Springer-Verlag, New York, 1993; second edition, Graduate Texts in Computer Science, Springer-Verlag, New York, 1997.
Computable structures: presentations matter; In the Scope of Logic, Methodology and the Philosophy of Science, Vol. 1, International Congress of LMPS, Cracow, August 1999 (P. Gardenfors, J. Wolenski and K. Kijania-Placek, eds.), Synthese Library 315, Kluwer Academic Publishers, Dordrecht, 2002, pp. 81–95.
Boolean algebras, invariants and ACA_0^+, Transactions of the American Mathematical Society 358 (2006), 989–1014.
Combinatorial principles weaker than Ramsey’s Theorem for pairs (with D. Hirschfeldt), Journal of Symbolic Logic 72 (2007), 171–206.
Degree structures: local and global investigations, Bulletin of Symbolic Logic 12 (2006), 369–389.
Local definability in degree structures: the Turing jump, hyperdegrees and beyond, Bulletin of Symbolic Logic 13 (2007), 226–239.