Weak One-Basedness

@article{Boxall2013WeakO,
  title={Weak One-Basedness},
  author={Gareth Boxall and David Bradley-Williams and Charlotte Kestner and Alexandra Omar Aziz and Davide Penazzi},
  journal={Notre Dame J. Formal Log.},
  year={2013},
  volume={54},
  pages={435-448}
}
We study the notion of weak one-basedness introduced in recent work of Berenstein and Vassiliev. Our main results are that this notion characterises linearity in the setting of geometric þ-rank 1 structures and that lovely pairs of weakly one-based geometric þ-rank 1 struc- tures are weakly one-based with respect to þ-independence. We also study geometries arising from infinite dimensional vector spaces over division rings. 
2 Citations

Weakly one-based geometric theories

Abstract We study the class of weakly locally modular geometric theories introduced in [4], a common generalization of the classes of linear SU-rank 1 and linear o-minimal theories. We find new

Geometric structures with a dense independent subset

We study a generalization of the expansion by an independent dense set, introduced by Dolich, Miller, and Steinhorn in the o-minimal context, to the setting of geometric structures. We introduce the

References

SHOWING 1-10 OF 13 REFERENCES

Weakly one-based geometric theories

Abstract We study the class of weakly locally modular geometric theories introduced in [4], a common generalization of the classes of linear SU-rank 1 and linear o-minimal theories. We find new

On lovely pairs of geometric structures

Generic pairs of SU-rank 1 structures

Definable structures in o-minimal theories: One dimensional types

Let N be a structure definable in an o-minimal structure M and p ∈ SN(N), a complete N-1-type. If dimM(p) = 1, then p supports a combinatorial pre-geometry. We prove a Zilber type trichotomy: Either

Properties and consequences of Thorn-independence

  • A. Onshuus
  • Mathematics
    Journal of Symbolic Logic
  • 2006
TLDR
It is proved that in any simple theory where the stable forking conjecture holds, ϸ-independence and forking independence agree.

Characterizing rosy theories

TLDR
It is shown that the existence of an ordinal valued equivalence relation rank is a (necessary and) sufficient condition for rosiness.

Dense pairs of o-minimal structures

The structure of definable sets and maps in dense elementary pairs of o-minimal expansions of ordered abelian groups is described. It turns out that a certain notion of “small definable set” plays a

A Geometric Introduction to Forking and Thorn-Forking

TLDR
The approach in this paper is to treat independence relations as mathematical objects worth studying, for a better understanding of thorn-forking, which turns out to be closely related to modular pairs in the lattice of algebraically closed sets.

Projective Geometry

  • G. M.
  • Mathematics
    Nature
  • 1911
IN the first page of their introduction the authors say:Projective Geometry.By Prof. O. Veblen Prof. J. W. Young. Vol. i. Pp. x + 342. (Boston and London: Ginn and Co., 1910.) Price 15s. net.

Simple Theories