Effective topos

In mathematics, the effective topos is a topos introduced by Martin Hyland (1982), based on Kleene's notion of recursive realizability, that captures the idea of effectivity in mathematics.

References

• Hyland, J. M. E. (1982), "The effective topos", in Troelstra, A. S.; Dalen, D. van, The L.E.J. Brouwer Centenary Symposium (Noordwijkerhout, 1981), Studies in Logic and the Foundations of Mathematics, 110, Amsterdam: North-Holland, pp. 165–216, doi:10.1016/S0049-237X(09)70129-6, ISBN 978-0-444-86494-9 
• Kleene, S. C. (1945). "On the interpretation of intuitionistic number theory". Journal of Symbolic Logic 10 (4): 109–124. doi:10.2307/2269016. 
• Phoa, Wesley (1992). An introduction to fibrations, topos theory, the effective topos and modest sets (Technical report). Laboratory for Foundations of Computer Science, University of Edinburgh. CiteSeerX 10.1.1.112.4533. ECS-LFCS-92-208.
• Bernadet, Alexis; Graham-Lengrand, Stéphane (2013). "A simple presentation of the effective topos". arXiv:1307.3832.