Later Developments
Kreisel introduced modified realizability, which uses typed lambda calculus as the language of realizers. Modified realizability is one way to show that Markov's principle is not derivable in intuitionistic logic. On the contrary, it allows to constructively justify the principle of independence of premiss:
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Relative realizability is an intuitionist analysis of recursive or recursively enumerable elements of data structures that are not necessarily computable, such as computable operations on all real numbers when reals can be only approximated on digital computer systems.
Read more about this topic: Realizability
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