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# Index Sets in Recursive Combinatorics

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## 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.

## Keywords

Partial Order Bipartite Graph Greedy Algorithm Turing Machine Line Graph
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© Springer Science+Business Media New York 1993