Weak One-Basedness

Penazzi, Davide orcid iconORCID: 0000-0002-9732-1577, Boxall, Gareth, Kestner, Charlotte orcid iconORCID: 0000-0001-8976-2981, Omar Aziz, Alexandra and Bradley-Williams, David (2013) Weak One-Basedness. Notre Dame Journal of Formal Logic, 54 (3-4). pp. 435-448.

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Official URL: http://projecteuclid.org/euclid.ndjfl/1376053772


We study the notion of weak one-basedness introduced in recent work of Berenstein and Vassiliev. Our main results are that this notion characterizes linearity in the setting of geometric þ-rank 1structures and that lovely pairs of weakly one-based geometric þ-rank 1 structures are weakly one-based with respect to þ-independence. We also study geometries arising from infinite-dimensional vector spaces over division rings.

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