Finiteness classes arising from Ramsey-theoretic statements in set theory without choice

Joshua Brot; Mengyang Cao; David Fernández-Bretón

doi:10.1016/j.apal.2021.102961

Finiteness classes arising from Ramsey-theoretic statements in set theory without choice

Joshua Brot, Mengyang Cao, David Fernández-Bretón

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

4 Citas (Scopus)

Resumen

We investigate infinite sets that witness the failure of certain Ramsey-theoretic statements, such as Ramsey's or (appropriately phrased) Hindman's theorem; such sets may exist if one does not assume the Axiom of Choice. We obtain very precise information as to where such sets are located within the hierarchy of infinite Dedekind-finite sets.

Idioma original	Inglés
Número de artículo	102961
Publicación	Annals of Pure and Applied Logic
Volumen	172
N.º	6
DOI	https://doi.org/10.1016/j.apal.2021.102961
Estado	Publicada - jun. 2021
Publicado de forma externa	Sí

Acceder al documento

10.1016/j.apal.2021.102961

Otros archivos y enlaces

Enlace a la publicación en Scopus

Citar esto

@article{9bcc362554bd4e6cb05887519ca8feb3,

title = "Finiteness classes arising from Ramsey-theoretic statements in set theory without choice",

abstract = "We investigate infinite sets that witness the failure of certain Ramsey-theoretic statements, such as Ramsey's or (appropriately phrased) Hindman's theorem; such sets may exist if one does not assume the Axiom of Choice. We obtain very precise information as to where such sets are located within the hierarchy of infinite Dedekind-finite sets.",

keywords = "Amorphous set, Axiom of choice, Dedekind-finite set, Fraenkel–Mostowski model, Hindman's theorem, Ramsey's theorem",

author = "Joshua Brot and Mengyang Cao and David Fern{\'a}ndez-Bret{\'o}n",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2021",

month = jun,

doi = "10.1016/j.apal.2021.102961",

language = "Ingl{\'e}s",

volume = "172",

journal = "Annals of Pure and Applied Logic",

issn = "0168-0072",

publisher = "Elsevier",

number = "6",

}

TY - JOUR

T1 - Finiteness classes arising from Ramsey-theoretic statements in set theory without choice

AU - Brot, Joshua

AU - Cao, Mengyang

AU - Fernández-Bretón, David

PY - 2021/6

Y1 - 2021/6

N2 - We investigate infinite sets that witness the failure of certain Ramsey-theoretic statements, such as Ramsey's or (appropriately phrased) Hindman's theorem; such sets may exist if one does not assume the Axiom of Choice. We obtain very precise information as to where such sets are located within the hierarchy of infinite Dedekind-finite sets.

AB - We investigate infinite sets that witness the failure of certain Ramsey-theoretic statements, such as Ramsey's or (appropriately phrased) Hindman's theorem; such sets may exist if one does not assume the Axiom of Choice. We obtain very precise information as to where such sets are located within the hierarchy of infinite Dedekind-finite sets.

KW - Amorphous set

KW - Axiom of choice

KW - Dedekind-finite set

KW - Fraenkel–Mostowski model

KW - Hindman's theorem

KW - Ramsey's theorem

UR - http://www.scopus.com/inward/record.url?scp=85101665985&partnerID=8YFLogxK

U2 - 10.1016/j.apal.2021.102961

DO - 10.1016/j.apal.2021.102961

M3 - Artículo

AN - SCOPUS:85101665985

SN - 0168-0072

VL - 172

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 6

M1 - 102961

ER -

Finiteness classes arising from Ramsey-theoretic statements in set theory without choice

Resumen

Acceder al documento

Otros archivos y enlaces

Huella

Citar esto