Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The theory of classical realizability is a framework in which  can develop the proof-program correspondence. Using this framework,  show how to transform into programs the proofs in classical analysis with dependent choice and the existence of a ll ordering of the real line. The principal tools are: The notion of realizability algebra, which is a three-sorted variant of the ll known combinatory algebra of Curry. An adaptation of the method of forcing used in set theory to prove consistency results. Here, it is used in another way, to obtain programs associated with a ll ordering of R and the existence of a non trivial ultrafilter on N.
['Jean-Louis Krivine']
I am writing a research paper on a idea Realizability algebras : a program to well order R
[{"from": "human", "value": "I am writing a research paper on a idea Realizability algebras : a program to well order R"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The theory of classical realizability is a framework in which  can develop the proof-program correspondence. Using this framework,  show how to transform into programs the proofs in classical analysis with dependent choice and the existence of a ll ordering of the real line. The principal tools are: The notion of realizability algebra, which is a three-sorted variant of the ll known combinatory algebra of Curry. An adaptation of the method of forcing used in set theory to prove consistency results. Here, it is used in another way, to obtain programs associated with a ll ordering of R and the existence of a non trivial ultrafilter on N."}]