L. Birkedal and J. van Oosten. Relative and modified relative realizability. Annals of Pure and Applied Logic, 118(1-2):115-132, 2002. (Gzipped PostScript, 18 pages, 102315 bytes)

S. Awodey and L. Birkedal. Elementary axioms for local maps of toposes. Journal of Pure and Applied Algebra, 177(3):215-230, February 2003. (Gzipped PostScript, 15 pages, 105682 bytes)

L. Birkedal. Developing theories of types and computability via realizability. Electronic Notes in Theoretical Computer Science, 34, 2000. Available at http://www.elsevier.nl/locate/entcs/volume34.html. The pdf version has active hyperreferences and is therefore the preferred version for reading online. (Gzipped PostScript, 290 pages, 624492 bytes) (PDF, 2023216 bytes)

L. Birkedal and J. van Oosten. Relative and modified relative realizability. Preprint 1146, Department of Mathematics, Universiteit Utrecht, March 2000.

A. Bauer and L. Birkedal. Continuous functionals of dependent types and equilogical spaces. In P. Clote and H. Schwichtenberg, editors, Computer Science Logic, 14th Annual Conference of the EACSL, Fischbachau, Germany, August 21-26, 2000, volume 1862 of Lecture Notes in Computer Science. Springer, August 2000. (Gzipped PostScript, 15 pages, 89805 bytes)

L. Birkedal, J. van Oosten, G. Rosolini, and D.S. Scott, editors. Tutorial Workshop on Realizability Semantics, FLoC'99, Trento, Italy, 1999. Mathematical Structures in Computer Science, volume 12. Cambridge University Press, 2002.

S. Awodey, L. Birkedal, and D.S. Scott. Local realizability toposes and a modal logic for computability. Mathematical Structures in Computer Science, 12(3):319-334, 2002. (Gzipped PostScript, 16 pages, 106898 bytes)

L. Birkedal. Developing Theories of Types and Computability via Realizability. PhD thesis, School of Computer Science, Carnegie Mellon University, December 1999. Available as CMU Technical Report: CMU-CS-99-173.

L. Birkedal. A general notion of realizability. In Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science, Santa Barbara, California, June 2000. IEEE Computer Society. (Gzipped PostScript, 11 pages, 79119 bytes)

S. Awodey and L. Birkedal. Elementary axioms for local maps of toposes. Technical Report CMU-PHIL-103, Department of Philosophy, Carnegie Mellon University, November 1999. (Gzipped PostScript, 18 pages, 68921 bytes)

S. Awodey, L. Birkedal, and D.S. Scott. Local realizability toposes and a modal logic for computability. In L. Birkedal, J. van Oosten, G. Rosolini, and D.S. Scott, editors, Tutorial Workshop on Realizability Semantics, FLoC'99, Trento, Italy, 1999, volume 23 of Electronic Notes in Theoretical Computer Science. Elsevier, 1999. (Gzipped PostScript, 14 pages, 67529 bytes)

S. Awodey, L. Birkedal, and D.S. Scott. Local realizability toposes and a modal logic for computability. Technical Report CMU-PHIL-99, Department of Philosophy, Carnegie Mellon University, April 1999. (Gzipped PostScript, 14 pages, 67529 bytes)

A. Bauer, L. Birkedal, and D.S. Scott. Equilogical spaces. Theoretical Computer Science, 315(1):35-59, 2004. (Gzipped PostScript, 28 pages, 134002 bytes)

L. Birkedal, A. Carboni, G. Rosolini, and D.S. Scott. Type theory via exact categories. In Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science, pages 188-198, Indianapolis, Indiana, June 1998. IEEE Computer Society. (Gzipped PostScript, 11 pages, 50454 bytes)