Open Access
2013 Weak One-Basedness
Gareth Boxall, David Bradley-Williams, Charlotte Kestner, Alexandra Omar Aziz, Davide Penazzi
Notre Dame J. Formal Logic 54(3-4): 435-448 (2013). DOI: 10.1215/00294527-2143934


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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Gareth Boxall. David Bradley-Williams. Charlotte Kestner. Alexandra Omar Aziz. Davide Penazzi. "Weak One-Basedness." Notre Dame J. Formal Logic 54 (3-4) 435 - 448, 2013.


Published: 2013
First available in Project Euclid: 9 August 2013

zbMATH: 1282.03017
MathSciNet: MR3091664
Digital Object Identifier: 10.1215/00294527-2143934

Primary: 03C45
Secondary: 03C10 , 03C95

Keywords: geometric theory , independence , local modularity , one-based , stability theory , thorn-forking

Rights: Copyright © 2013 University of Notre Dame

Vol.54 • No. 3-4 • 2013
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