From a constructive perspective the many notions of Noetherianity and well quasi-order form a rich landscape, which we here explore. Besides the well-studied conditions about sequences, we include the finite basis property of the original Higman lemma, trying a first joint analysis of Noetherianity and well quasi-order in the spirit of reverse mathematics with intuitionistic logic. Applying a topological semantics for intuitionistic logic, we settle a conjecture by Ray Mines; moreover, by the realizability topos of infinite-time Turing machines, we separate the ascending chain condition with finite generation from the one without.
A Constructive Picture of Noetherian Conditions and Well Quasi-orders
Buriola, Gabriele;Schuster, Peter;Blechschmidt, Ingo
2023-01-01
Abstract
From a constructive perspective the many notions of Noetherianity and well quasi-order form a rich landscape, which we here explore. Besides the well-studied conditions about sequences, we include the finite basis property of the original Higman lemma, trying a first joint analysis of Noetherianity and well quasi-order in the spirit of reverse mathematics with intuitionistic logic. Applying a topological semantics for intuitionistic logic, we settle a conjecture by Ray Mines; moreover, by the realizability topos of infinite-time Turing machines, we separate the ascending chain condition with finite generation from the one without.
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