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arXiv · 2104.13910

Notions of indifference for genericity: Union and subsequence sets

Tejas Bhojraj
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Abstract

A set $I$ is said to be a universal indifferent set for $1$-genericity if for every $1$-generic $G$ and for all $X \subseteq I$, $G \Delta X$ 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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Tejas Bhojraj. 2021-04-28. Notions of indifference for genericity: Union and subsequence sets. https://doi.org/10.1093/logcom/exab035

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