Abstract
Many theorems in infinite combinatorics have noneffective proofs. Nerode’s recursive mathematics program [10] involves looking at noneffective proofs and seeing if they can be made effective. The framework is recursion-theoretic. Typically, if a theorem has a noneffective proof, one would find a ‘recursive version’ of it and see if it is true. Usually the recursive version is false, hence the original proof is necessarily noneffective.
Supported in part by NSF grants CCR-8803641 and CCR-9020079.
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© 1993 Springer Science+Business Media New York
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Gasarch, W., Martin, G. (1993). Index Sets in Recursive Combinatorics. In: Crossley, J.N., Remmel, J.B., Shore, R.A., Sweedler, M.E. (eds) Logical Methods. Progress in Computer Science and Applied Logic, vol 12. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0325-4_11
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DOI: https://doi.org/10.1007/978-1-4612-0325-4_11
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