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The Spectrum of the Γ-Invariant of a Bilinear Space

✍ Scribed by James E Baumgartner; Matthew Foreman; Otmar Spinas

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
245 KB
Volume
189
Category
Article
ISSN
0021-8693

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✦ Synopsis

To every symmetric bilinear space X, of regular uncountable dimension , Ž . Ž . Ž . Ž Ž .

. an invariant ⌫ X, g P P rF F where F F is the club filter can be assigned. We prove that in dimension / the spectrum of ⌫ cannot be determined in 2 ZFC. For this, on the one hand we show that under CH, ⌫ attains the maximal Ž . 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 , the spectrum of ⌫ in dimension / is much thinner than the maximal one. 2 2

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