Maths Research Associates 2021 East Anglia

Lead Research Organisation: University of East Anglia
Department Name: Mathematics

Abstract

Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.

Publications

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Aslanyan V (2023) Independence relations for exponential fields in Annals of Pure and Applied Logic

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Aslanyan V (2022) Independence relations for exponential fields

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DMITRIEVA A (2023) DIVIDING LINES BETWEEN POSITIVE THEORIES in The Journal of Symbolic Logic

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Kamsma M (2023) Bilinear spaces over a fixed field are simple unstable in Annals of Pure and Applied Logic

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Kamsma M (2022) Bilinear spaces over a fixed field are simple unstable

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KAMSMA M (2022) NSOP-LIKE INDEPENDENCE IN AECATS in The Journal of Symbolic Logic

 
Description Important tools in model theory, a branch of mathematical logic, have been successfully generalised to logical frameworks that are more general than the traditional framework in which classical model theory operates. In particular, the results concern independence relations. Concrete examples of such independence relations are linear independence and probabilistic independence. Using category theory, another field in mathematics, the work proves that certain categories can only have one nice independence relation. This is then further applied towards a model-theoretic study of independence relations for mathematical structures where this was previously impossible.
Exploitation Route There are essentially two flavours of results arising from this work. The first is very general abstract theory, while the second applies this general abstract theory in concrete cases. The first flavour allows for further exploration of deep model-theoretic ideas in this new generality. At the same time it allows for the application of the already developed model-theoretic tools in places where this was not possible before. The second flavour is an example of this and can also be used by researchers as such. Additionally, the latter flavour also vastly improves our understanding of the mathematical structures involved, which helps future researchers understand and potentially answer open questions about these particular structures.
Sectors Other
URL https://arxiv.org