Independence and bases: theme and variations. (English) Zbl 07902057
Summary: 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.
MSC:
| 03C35 | Categoricity and completeness of theories |
| 05B35 | Combinatorial aspects of matroids and geometric lattices |
| 20B10 | Characterization theorems for permutation groups |
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