Notions of indifference for genericity: Union and subsequence sets
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A set I is said to be a universal indifferent set for 1-genericity if for every 1-generic G and for all X ⊆ I, G Δ X is also 1-generic. Miller showed that there is no infinite universal indifferent set for 1-genericity. We introduce two variants (union and subsequence sets for 1-genericity) of the notion of universal indifference and prove that there are no non-trivial universal sets for 1-genericity with respect to these notions. In contrast, we show that there is a non-computable subsequence set for weak-1-genericity.
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