# Games in Recursion Theory and Continuity Properties of Capping Degrees

@inproceedings{Harrington1992GamesIR, title={Games in Recursion Theory and Continuity Properties of Capping Degrees}, author={Leo Harrington and Robert I. Soare}, year={1992} }

It is shown here that there are no maximal minimal pairs of recursively enumerable (r.e.) degrees. Combining this with a dual theorem by Ambos-Spies, Lachlan and Soare for r.e. degrees cupping to 0′ it follows that any open formula F(x, y) of two free variables in the language of the r.e. degrees, R, which holds for r.e. degrees a ≠ b, where a, b ≠ 0,0’, holds continuously in a neighborhood about a and b. This is the best possible continuity result for formulas in general, because it fails for… CONTINUE READING

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