TY - JOUR
T1 - Hindman's theorem in the hierarchy of choice principles
AU - Fernández-Bretón, David
N1 - Publisher Copyright:
© 2023 World Scientific Publishing Company.
PY - 2023
Y1 - 2023
N2 - In the context of ZF, we analyze a version of Hindman's finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various classical weak choice principles, thus precisely locating the strength of the statement as a weak form of the AC.
AB - In the context of ZF, we analyze a version of Hindman's finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various classical weak choice principles, thus precisely locating the strength of the statement as a weak form of the AC.
KW - Fraenkel-Mostowski model
KW - Hindman's theorem
KW - Weak choice principles
KW - choiceless set theory
UR - http://www.scopus.com/inward/record.url?scp=85150732121&partnerID=8YFLogxK
U2 - 10.1142/S0219061323500022
DO - 10.1142/S0219061323500022
M3 - Artículo
AN - SCOPUS:85150732121
SN - 0219-0613
JO - Journal of Mathematical Logic
JF - Journal of Mathematical Logic
M1 - 2350002
ER -