Taranovsky's ordinal notations: Difference between revisions
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RhubarbJayde (talk | contribs) (Created page with "Taranovsky's ordinal notations are a collection of ordinal notation systems invented by Dmytro Taranovsky. These include degrees of recursive inaccessibility (DoRI), degrees of reflection (DoR) and the main system (MS), as well as variants such as degrees of reflection with passthrough.<ref>https://web.mit.edu/dmytro/www/other/OrdinalNotation.htm</ref> They all use a binary or ternary function symbol \(C\), but the comparison algorithms and ot...") |
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These were conjectured originally to be very strong, with the main system possibly reaching the full strength of [[second-order arithmetic]] and beyond. However, it is believed that, due to missing some [[Gandy ordinal|bad ordinal]] structure and other issues, the system may not even reach the subsystem of \(\Pi^1_2\)-comprehension.
One of the systems, '''MP''' (Main System with Passthrough), is known to be ill-founded.
== DoRI ==
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