Index Sets in Recursive Combinatorics
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Many theorems in infinite combinatorics have noneffective proofs. Nerode’s recursive mathematics program  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.
KeywordsPartial Order Bipartite Graph Greedy Algorithm Turing Machine Line Graph
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- Kierstead, H.A. , Recursive ordered sets. In Combinatorics and Ordered Sets, vol. 57 of Contemporary Mathematics. American Mathematical Society.Google Scholar
- König, D. , Sur les correspondances multivoques des ensembles, Fundamenta Mathematicae 26, 114–130.Google Scholar
- Soare, R.I. , Recursively Enumerable Sets and Degrees. Perspectives in Mathematical Logic. Springer-Verlag, Berlin.Google Scholar
- Specker, E. , Ramsey’s Theorem does not hold in recursive set theory. In Logic Colloquium; 1969 Manchester, 439–442.Google Scholar