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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.

3 votes
1 answer
164 views

What's the measure of all 1-generic sets?

A set $A$ is 1-generic if it forces its jump, namely for any $e\in\omega$, there exists $\sigma\preceq A$ such that: $\Phi^{\sigma}_{e}(e)\downarrow\vee(\forall\tau\succeq\sigma)(\Phi^{\tau}_{e}(e)\up …
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