Content deleted Content added
BartekChom (talk | contribs) |
→top: Expanding article |
||
Line 1:
In [[mathematics]], a '''Mahlo cardinal''' is a certain kind of [[large cardinal]] number. Mahlo cardinals were first described by {{harvs|txt|authorlink= Paul Mahlo|first=Paul|last=Mahlo|year1=1911|year2=1912|year3=1913}}. As with all large cardinals, none of these varieties of Mahlo cardinals can be proved to exist by [[ZFC]] (assuming ZFC is consistent).
A [[cardinal number]] κ is called ''strongly Mahlo'' if κ is [[inaccessible cardinal|strongly inaccessible]] and the [[Set (mathematics)|set]] U = {λ < κ: λ is strongly inaccessible} is [[stationary set#Classical notion|stationary]] in κ.
A cardinal κ is called ''weakly Mahlo'' if κ is weakly inaccessible and the set of weakly inaccessible cardinals less than κ is stationary in κ.
The term "Mahlo cardinal" now usually means "strongly Mahlo cardinal", though the cardinals originally considered by Mahlo were weakly Mahlo cardinals.
== Minimal condition sufficient for a Mahlo cardinal ==
| |||