Noetherian theories

Amador Martin-Pizarro; Martin Ziegler

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arXiv · 2307.16826

Noetherian theories

Amador Martin-Pizarro·Martin Ziegler

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Abstract

A first-order theory is Noetherian with respect to the collection of formulae $\mathcal{F}$ if every definable set is a Boolean combination of instances of formulae in $\mathcal{F}$ and the topology whose subbasis of closed sets is the collection of instances of arbitrary formulae in $\mathcal{F}$ is Noetherian. Noetherianity is a strengthening of equationality, which itself implies stability. We show the Noetherianity of the theory of proper pairs of algebraically closed fields in any characteristic.

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BibTeX RIS

Amador Martin-Pizarro, Martin Ziegler. 2023-07-31. Noetherian theories. https://arxiv.org/abs/2307.16826

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