The Spectrum of the Γ-Invariant of a Bilinear Space Original Research Article

To every symmetric bilinear space (X, φ) of regular uncountable dimension κ, an invariant Γ(X, φ) set membership, variant image(κ)/image (κ) (where image (κ) is the club filter) can be assigned. We prove that in dimension aleph, Hebrew2the 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 Mitchellʹs model, which is obtained by collapsing a weakly compact cardinal to ω2, the spectrum of Γ in dimension aleph, Hebrew2is much thinner than the maximal one.