caa a22 4500 469068515 CHVBK 20180323132915.0 cr unu---uuuuu 170328e19921001xx s 000 0 eng 10.1007/BF02808222 doi (NATIONALLICENCE)springer-10.1007/BF02808222 Spinas O. Abteilung Mathematik, ETH-Zentrum, 8092, Zürich, Switzerland aut Iterated forcing in quadratic form theory [Elektronische Daten] [O. Spinas] In [Sp1] and [B/Sp] it has been shown that the existence of quadratic spaces of uncountable dimension over finite or countable fields sharing the property that every infinite dimensional subspace has its orthogonal complement of at most countable dimension is independent of the axioms of ZFC set theory. Such a space will be called astrong Gross space in the sequel. Cardinal invariants of the continuum decide whether strong Gross spaces exist or not. Namely, when b=ω1 a strong Gross space of dimension ℵ1 exists. When p>ω1 such spaces do not exist. Here we answer the question what happens with strong Gross spaces in case b>ω1 or p=ω1. Hebrew University, 1992 Israel Journal of Mathematics Springer-Verlag 79/2-3(1992-10-01), 297-315 0021-2172 79:2-3<297 1992 79 11856 https://doi.org/10.1007/BF02808222 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02808222 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Spinas O. Abteilung Mathematik, ETH-Zentrum, 8092, Zürich, Switzerland aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer-Verlag 79/2-3(1992-10-01), 297-315 0021-2172 79:2-3<297 1992 79 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer