Independence and bases: theme and variations

Peter J. Cameron

doi:10.2140/mt.2024.3.417

Independence and bases: theme and variations

Peter J. Cameron^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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Abstract

This paper describes a complex of related ideas, ranging from Urbanik's v*-algebras, through Deza's geometric groups and Zilber's homogeneous geometries, to Sims' bases for permutation groups and their use in defining "size" parameters on finite groups, with a brief look at Cherlin's relational complexity. It is not a complete survey of any of these topics, but aims to describe the links between them.

Original language	English
Pages (from-to)	417-431
Number of pages	15
Journal	Model Theory
Volume	3
Issue number	2
DOIs	https://doi.org/10.2140/mt.2024.3.417
Publication status	Published - 19 Jul 2024

Keywords

Independence
Bases
Independence algebras
Relational complexity
Strictly minimal structures

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10.2140/mt.2024.3.417

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Copyright © 2023 Publisher / the Author(s). This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.2140/mt.2024.3.417.
Licence: CC BY

Cite this

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AB - This paper describes a complex of related ideas, ranging from Urbanik's v*-algebras, through Deza's geometric groups and Zilber's homogeneous geometries, to Sims' bases for permutation groups and their use in defining "size" parameters on finite groups, with a brief look at Cherlin's relational complexity. It is not a complete survey of any of these topics, but aims to describe the links between them.

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KW - Bases

KW - Independence algebras

KW - Relational complexity

KW - Strictly minimal structures

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JO - Model Theory

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Independence and bases: theme and variations

Abstract

Keywords

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