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Results tagged with genericity
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user 23648
Questions about notions of genericity in computability theory/descriptive set theory. Not restricted to the 'standard' partial order producing $\alpha$-generics. Use the forcing tag for set-theoretic forcing.
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Are the $\omega$-generic arithmetic degrees downward closed
A degree is $\alpha$-generic if it has representative that is $\alpha$-generic. Are the $\omega$-generic arithmetic degrees (i.e. the degree structure induced by arithmetic reproducibility) downward …
- 3,029
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Accepted
Cite for fact that every r.e. degree bounds a 1-generic
For the benefit of others, I emailed Shore and asked him about it and he told me that while he had assumed when he proved it that it wasn't a novel result he never actually found any earlier proof (mu …
- 3,029
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119
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Cite for fact that every r.e. degree bounds a 1-generic
Odifreddi doesn't give a cite (at least in proposition XI.2.10) for the proposition that every non-zero r.e. degree computes a 1-generic. What paper should I cite for this proposition?
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Kurtz randomness and supermartingales with infinite *limit*
Suppose you replace the usual success conditions for a supermartingale (lim sup is infinite) with the requirement that the actual limit is infinite, e.g. a supermartingale $B$ succeeds on $X \in 2^\om …
- 3,029