Archivio Istituzionale della RicercaThe axiom of dependent choice (DC) and the axiom of countable choice (AC_ω) are two weak forms of the axiom of choice that can be stated for a specific set: DC(X)asserts that any total binary relation on X has an infinite chain, while AC_ω(X) asserts that any countable collection of nonempty subsets of X has a choice function. It is well-known that DC implies AC_ω. We study for which sets and under which hypotheses DC(X)double right arrow AC_ω(X) and then we show it is consistent with ZF that there is a set A subset of R for which DC(A) holds, but AC_ω(A) fails
Does DC imply AC_ω, uniformly? / Andretta, Alessandro; Notaro, Lorenzo. - In: THE JOURNAL OF SYMBOLIC LOGIC. - ISSN 0022-4812. - ELETTRONICO. - 90:4(2025), pp. 1-25. [10.1017/jsl.2024.33]
Does DC imply AC_ω, uniformly?
LORENZO NOTARO
2025
Abstract
The axiom of dependent choice (DC) and the axiom of countable choice (AC_ω) are two weak forms of the axiom of choice that can be stated for a specific set: DC(X)asserts that any total binary relation on X has an infinite chain, while AC_ω(X) asserts that any countable collection of nonempty subsets of X has a choice function. It is well-known that DC implies AC_ω. We study for which sets and under which hypotheses DC(X)double right arrow AC_ω(X) and then we show it is consistent with ZF that there is a set A subset of R for which DC(A) holds, but AC_ω(A) fails
| File | Dimensione | Formato | |
|---|---|---|---|
|
does-dollarmathsf-dcdollar-imply-dollarmathsf-acomega-dollar-uniformly.pdf
accesso aperto
Tipologia:
2a Post-print versione editoriale / Version of Record
Licenza:
Creative commons
Dimensione
335.52 kB
Formato
Adobe PDF
|
335.52 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11583/2992785