Abstract
To every symmetric bilinear space (X,φ) of regular uncountable dimension κ, an invariant Γ(X,φ)∈P(κ)/F(κ) (where F(κ) is the club filter) can be assigned. We prove that in dimension ℵ2the spectrum of Γ cannot be determined inZFC. For this, on the one hand we show that underCH, Γ attains the maximal (with respect to a restriction provable inZFC) spectrum; we also show thatCHis not necessary for this result. On the other hand we show that in a variation of Mitchell's model, which is obtained by collapsing a weakly compact cardinal to ω2, the spectrum of Γ in dimension ℵ2is much thinner than the maximal one.
Sign-in/Register to access full text options 
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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
