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Reconstruction of classical geometries from their automorphism group

Barbina, S. (2007). Reconstruction of classical geometries from their automorphism group. Journal of the London Mathematical Society, 75(2) pp. 298–316.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1112/jlms/jdl016
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Abstract

Let V be a countably infinite-dimensional vector space over a finite field F. Then V is omega-categorical, and so are the projective space PG(V) and the projective symplectic, unitary and orthogonal spaces on V. Using a reconstruction method developed by Rubin, we prove the following result: let M be one of the above spaces, and let N be an omega-categorical structure such that Aut(M) and Aut(N) are isomorphic as abstract groups. Then M and N are bi-interpretable. We also give a reconstruction result for the affine group AGL(V) acting on V by proving that V as an affine space is interpretable in AGL(V).

Item Type: Journal Article
Copyright Holders: 2007 London Mathematical Society
ISSN: 1469-7750
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Related URLs:
Item ID: 30741
Depositing User: Silvia Barbina
Date Deposited: 11 Jan 2012 14:49
Last Modified: 11 Jan 2012 14:49
URI: http://oro.open.ac.uk/id/eprint/30741
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