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Results tagged with forcing
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user 23648
Forcing is a method first used to prove the continuum hypothesis is independent of the classical axioms of set theory
2
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1
answer
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Arithmetically-hyperimmune-free degrees are comeager
I think proposition XIII.1.22 of Odifreddi is false but I wanted to check I wasn't being dumb. Here's the claim.
Definition: The set$^1$ $A$ is arithmetically-hyperimmune-free if every function $f$ a …
- 3,029
2
votes
Accepted
Arithmetically-hyperimmune-free degrees are comeager
Absent any pushback and based on some further reading I'm going to say this claim is false and the correct claim is that the arithmetically-hyperimmune-free degrees have measure 0.
- 3,029
3
votes
On Applications of Forcing in Domain Theory
Note that forcing techniques are frequently used in computability theory, e.g., to establish the existence of degrees with certain properties. … In particular, forcing arguments can be thought of as applications of (a version of) the Baire Category Theorem. …
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2
votes
1
answer
139
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Are Cohen Generics Minimal Covers?
I'm ultimately interested in this question for some more effective notion of forcing but I realized I wasn't sure how to show this even assuming full set-theoretic forcing (with the reduction being relative … If using full set-theoretic forcing introduces complications I'm fine with just forcing with respect to hyperarithmetic statements (i.e., $\omega_1$ generics in the sense of Fefferman and the reduction …
- 3,029