Abstract
Theorem. There is a countable admissible set, Ol , with ordinal ω CK 1 such that if S is Sacks generic over Ol then ω 1 S > ω CK 1 and S is a nonminimal upper bound for the hyperdegrees in Ol . (The same holds over Ol for any upper bound produced by any forcing which can be construed so that the forcing relation for Σ 1 formulas is Σ 1.) A notion of forcing, the “delayed collapse” of ω CK 1, is defined. The construction hinges upon the symmetries inherent in how this forcing interacts with Σ 1 formulas. It also uses Steel trees to make a certain part of the generic object Σ 1 over the final inner model, Ol , and, indeed, over many generic extensions of Ol .
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
