Affiliation:
1. Department of Mathematics, University of Wisconsin–Madison, 480 Lincoln Dr., Madison, WI 53706, USA
Abstract
Abstract
A set $I$ is said to be a universal indifferent set for $1$-genericity if for every $1$-generic $G$ and for all $X \subseteq I$, $G \varDelta X$ is also $1$-generic. Miller (2013, The Journal of Symbolic Logic, 78, 113–138) 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.
Publisher
Oxford University Press (OUP)
Subject
Logic,Hardware and Architecture,Arts and Humanities (miscellaneous),Software,Theoretical Computer Science
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