In mathematics, the effective topos is a topos introduced by MartinHyland(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, ISBN978-0-444-86494-9, MR717245
Kleene, S. C. (1945). "On the interpretation of intuitionistic number theory". Journal of Symbolic Logic10 (4): 109–124. doi:10.2307/2269016. JSTOR2269016.
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