NOTES ON THE DPRM PROPERTY FOR LISTABLE STRUCTURES

Simple item page
dc.contributor.authorPasten, Hector
dc.date.accessioned2025-01-20T22:00:30Z
dc.date.available2025-01-20T22:00:30Z
dc.date.issued2022
dc.description.abstractA celebrated result by Davis, Putnam, Robinson, and Matiyasevich shows that a set of integers is listable if and only if it is positive existentially definable in the language of arithmetic. We investigate analogues of this result over structures endowed with a listable presentation. When such an analogue holds, the structure is said to have the DPRM property. We prove several results addressing foundational aspects around this problem, such as uniqueness of the listable presentation, transference of the DPRM property under interpretation, and its relation with positive existential bi-interpretability. A first application of our results is the rigorous proof of (strong versions of) several folklore facts regarding transference of the DPRM property. Another application of the theory we develop is that it will allow us to link various Diophantine conjectures to the question of whether the DPRM property holds for global fields. This last topic includes a study of the number of existential quantifiers needed to define a Diophantine set.
dc.description.funderANID (ex CONICYT) FONDECYT Regular from Chile
dc.fuente.origenWOS
dc.identifier.doi10.1017/jsl.2021.97
dc.identifier.eissn1943-5886
dc.identifier.issn0022-4812
dc.identifier.urihttps://doi.org/10.1017/jsl.2021.97
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/93730
dc.identifier.wosidWOS:000749919300001
dc.issue.numero1
dc.language.isoen
dc.pagina.final312
dc.pagina.inicio273
dc.revistaJournal of symbolic logic
dc.rightsacceso restringido
dc.subjectDiophantine set
dc.subjectlistable structure
dc.subjectglobal fields
dc.titleNOTES ON THE DPRM PROPERTY FOR LISTABLE STRUCTURES
dc.typeartículo
dc.volumen87
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
Files
Collections
Artículos de revistas