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.
2023
978-3-031-36977-3
Constructive mathematics, chain conditions, well quasi-order, finite generation, inductive definition
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1105546
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? ND
social impact