Taranovsky's ordinal notations: Difference between revisions
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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. |
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. |
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One of the systems, '''MP''' (Main System with Passthrough), is known to be ill-founded. |
One of the systems, '''MP''' (Main System with Passthrough), is known to be ill-founded.<ref>Discord message in #taranovsky-notations</ref> |
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== DoRI == |
== DoRI == |
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