Qualifications & Memberships
Research interests include: constructive foundations of mathematics: in particular, constructive foundations of analysis (real and functional) and topology (the axiomatic theory of apartness), and ring theory; constructive reverse mathematics: classifying constructive proofs by the principles they require, and nonconstructive proofs by the nonconstructive principles they depend on; computability and abstract complexity theory; mathematical economics: the numerical representation of preference relations; demand functions; equilibrium theory; and quantum logic and operator-theoretic foundations of physics.
- Baroni MA. and Bridges DS. (2008) Continuity Properties of Preference Relations. Electronic Notes in Theoretical Computer Science 202: 19-25. http://dx.doi.org/10.1016/j.entcs.2008.03.004.
- Baroni MA. and Bridges DS. (2008) Continuity properties of preference relations. Mathematical Logic Quarterly 54(5): 454-459. http://dx.doi.org/10.1002/malq.200710059.
- Berger J. and Bridges D. (2008) The anti-Specker property, a Heine-Borel property, and uniform continuity. Archive for Mathematical Logic 46(7-8): 583-592. http://dx.doi.org/10.1007/s00153-007-0063-1.
- Berger J. and Bridges D. (2008) The Fan Theorem and Positive-Valued Uniformly Continuous Functions on Compact Intervals. New Zealand Journal of Mathematics 38: 129-135. http://nzjm.math.auckland.ac.nz/ images/1/ 1f/The_Fan_Theorem_and_Positive-Valued_Uniformly_Continuous_Functions_on_Compact_Intervals.pdf.
- Bridges D., Ishihara H., Schuster PM. and Vita L. (2008) Apartness, compactness and nearness. Theoretical Computer Science 405(1-2): 3-10. http://dx.doi.org/10.1016/j.tcs.2008.06.019.