constructive mathematics, realizability, computability
propositions as types, proofs as programs, computational trinitarianism
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Vladimir Lifschitz, $CT_0$ is stronger than $CT_0!$. Proceedings of the American Mathematical Society, Volume 73, Number 1, January 1979, pp. 101–106. [pdf]
Jaap van Oosten, Lifschitz realizability. The Journal of Symbolic Logic, Volume 55, Issue 2 (1990), pp. 805-821. [doi:10.2307/2274666]
Jaap van Oosten, Two remarks on the Lifschitz realizability topos. The Journal of Symbolic Logic, Volume 61, Issue 1, March 1996, pp. 70-79. [doi:10.2307/2275598]
Ray-Ming Chen?, Michael Rathjen, Lifschitz realizability for intuitionistic Zermelo-Fraenkel set theory. Archive for Mathematical Logic, Volume 51 (2012), pp. 789–818. [doi:10.1007/s00153-012-0299-2, pdf]
Michael Rathjen, Andrew Swan, Lifschitz Realizability as a Topological Construction. The Journal of Symbolic Logic, Volume 85, Issue 4, December 2020, pp. 1342 - 1375. [doi:10.1017/jsl.2021.1, arXiv:1806.10047]
Takayuki Kihara, Degrees of incomputability, realizability and constructive reverse mathematics [arXiv:2002.10712]
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