On Gross Spaces

@article{Shelah1995OnGS,
  title={On Gross Spaces},
  author={Saharon Shelah and Otmar Spinas},
  journal={arXiv: Logic},
  year={1995}
}
A Gross space is a vector space E of infinite dimension over some field F, which is endowed with a symmetric bilinear form � : E 2 → F and has the property that every infinite dimensional subspace U ⊆ E satisfies dimU ⊥ < dimE. Gross spaces over uncountable fields exist (in certain dimen- sions) (see (G/O)). The existence of a Gross space over countable or finite fields (in a fixed dimension not above the continuum) is independent of the axioms of ZFC. This was shown in (B/G), (B/Sp) and (Sp2… 
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