The spectrum of the Gamma-invariant of a bilinear space

[摘要] To every symmetric bilinear space (X, phi) of regular uncountable dimension kappa, an invariant Gamma(X, phi) is an element of P(kappa)/F(kappa) (where F(kappa) is the club filter) can be assigned. We prove that in dimension aleph(2) the spectrum of Gamma cannot be determined in ZFC. For this, on the one hand we show that under CH, Gamma attains the maximal (with respect to a restriction provable in ZFC) spectrum; we also show that CH is 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 omega(2) the spectrum of Gamma in dimension aleph(2) is much thinner than the maximal one. (C) 1997 Academic Press.

[发布日期] 1997-03-15