Kinds of pregeometries of acyclic theories

Sergey B. Malyshev

The Bulletin of Irkutsk State University. Series Mathematics, Tome 46 (2023), pp. 110-120

Résumé

The article is devoted to the description of types of pregeometries with an algebraic closure operator for acyclic theories. In these theories we describe conditions of violation of the exchange property for a pregeometry. Taking into account these conditions, we introduce new concepts that do not rely on the exchange property: $a$-pregeometry, $a$-modularity, etc. The dependence conditions for an $a$-modular and $a$-locally finite $a$-pregeometry on the number of non-isomorphic trees and special points are established. Sufficient conditions of dependence for a $a$-local finite $a$-pregeometry on the vertices of the $a$-type are established, too.

Détail

Keywords: pregeometry, cyclic theory, $a$-pregeometry, $a$-modularity, $a$-locally finite, special vertices, $A$-special vertices.

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