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Needed reals and recursion in generic reals

✍ Scribed by Andreas Blass

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
107 KB
Volume
109
Category
Article
ISSN
0168-0072

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✦ Synopsis

We consider sets of reals that are "adequate" in various senses, for example dominating or unbounded or splitting or non-meager. Call a real x "needed" (in any of these senses) if every adequate set contains a real in which x is recursive. We characterize the needed reals for numerous senses of "adequate." We also consider, for various notions of forcing that add reals, the problem of characterizing the ground-model reals that are recursive in generic reals.

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