Taranovsky's ordinal notations: Difference between revisions

== Main system ==

The main system is divided into infinitely many subsystems. The zeroth subsystem has limit [[Epsilon numbers|\(\varepsilon_0\)]], the first subsystem has limit [[Bachmann-Howard ordinal|BHO]]<nowiki>, and the second subsystem's limit is greater than the limit of DoR. While an obsolete analysis suggested the limit was beyond a nonprojectible ordinal, the current best lower bound on its strength is slightly greater than an ordinal \(\alpha\) which is \(\beta\)-stable, where \(\beta > \alpha\) and \(\beta\) is \(\omega_{\beta^+}^{\mathrm{CK}}\)-stable.</nowiki>