Submission date: 31 July 2023

Abstract:

A first-order theory is Noetherian with respect to the collection of formulae F if every definable set is a Boolean combination of instances of formulae in F and the topology whose subbasis of closed sets is the collection of instances of arbitrary formulae in 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.

Mathematics Subject Classification: 03C45, 12H05

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Full text arXiv 2307.16826: pdf, ps.