Research Interests

My interests are in Logic and Computable Structure Theory. Initially, my research was in model theory. I did some work on models of arithmetic and infinitary logic. Gradually, my interests shifted to computability. Currently, I am interested in the relationship between computability and definability in familiar kinds of mathematical structures: linear orderings, vector spaces, etc. I am also interested in abstract problems on the technology used in this area.

My students have obtained results on computability questions about groups, Boolean algebras, and models of arithmetic.

Selected Publications

• C. J. Ash and J. F. Knight, Computable Structures and the Hyperarithmetical Hierarchy, Elsevier, 2000.
• J. F. Knight and M. Stob, Computable Boolean algebras, J. Symb. Logic, vol. 65 (2000), pp.1605-1623.
• J. F. Knight, "Minimality and completions of PAA", J. Symb. Logic, vol. 66 (2001), pp. 1447-1457.
• J. F. Knight, "Sequences of degrees associated with models of arithmetic", to appear in Logic Colloquium, 2001, ed. by S. Friedman.
• V. S. Harizanov, J. F. Knight, and A. S. Morozov, "Sequences of n-diagrams", to appear in J. Symb. Logic.