Effective topos

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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.


  • Hyland, J. M. E. (1982), "The effective topos", in Troelstra, A. S.; Dalen, D. van (eds.), 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, MR 0717245
  • Kleene, S. C. (1945). "On the interpretation of intuitionistic number theory". Journal of Symbolic Logic. 10 (4): 109–124. doi:10.2307/2269016. JSTOR 2269016.
  • Phoa, Wesley (1992), An introduction to fibrations, topos theory, the effective topos and modest sets
  • Bernadet, Alexis; Graham-Lengrand, Stéphane (2013). "A simple presentation of the effective topos". arXiv:1307.3832.