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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2023. Vol 46

Kinds of Pregeometries of Acyclic Theories

Author(s)
Sergey B. Malyshev1

1Novosibirsk State Technical University, Novosibirsk, Russian Federation

Abstract
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.
About the Authors
Sergey B. Malyshev, Novosibirsk State Technical University, Novosibirsk, 630073, Russian Federation, sergei2-mal1@yandex.ru
For citation
Malyshev S. B. Kinds of Pregeometries of Acyclic Theories. The Bulletin of Irkutsk State University. Series Mathematics, 2023, vol. 46, pp. 110–120. https://doi.org/10.26516/1997-7670.2023.46.110
Keywords
pregeometry, cyclic theory, 𝑎-pregeometry, 𝑎-modularity, 𝑎-locally finite, special vertices, 𝐴-special vertices
UDC
510.67
MSC
03C30, 03C65, 51D05
DOI
https://doi.org/10.26516/1997-7670.2023.46.110
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