Noetherian theories
Logic
2024-08-14 v4
Abstract
A first-order theory is Noetherian with respect to the collection of formulae if every definable set is a Boolean combination of instances of formulae in and the topology whose subbasis of closed sets is the collection of instances of arbitrary formulae in 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.
Keywords
Cite
@article{arxiv.2307.16826,
title = {Noetherian theories},
author = {Amador Martin-Pizarro and Martin Ziegler},
journal= {arXiv preprint arXiv:2307.16826},
year = {2024}
}