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Thesis

A model-theoretic approach to the arithmetic of global fields

Abstract:

This thesis assembles some new results in the field arithmetic of various classes of fields, including global fields, models of the common first-order theory of algebraic extensions of global fields, and fields of finite transcendence degree over their prime field. Most of the results stem from a very simple technique for first-order definitions in fields, based on the satisfaction of a first-order sentence in a family of finite extensions of the ground field. In the first two chapters, we...

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Division:
MPLS
Department:
Mathematical Institute
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Author

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Department:
University of Oxford
Role:
Supervisor
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Funding agency for:
Dittmann, P
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Funding agency for:
Dittmann, P
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford
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UUID:
uuid:c798e052-b305-4cca-8964-e7959e486a5d
Deposit date:
2019-01-31

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