Talk: Takeuti-Feferman-Buchholz ordinal

Is this ordinal comparable to \(\psi_{\Omega_1}(\Omega_\omega)\)? Ikosarakt1 (talk ^ contribs) 19:40, March 30, 2013 (UTC)

First of all, I wanted to ask if \(\psi_i(\alpha)\) function is same as described here? If so, TFB ordinal is strictly larger, because it is limit of Buchholz's collapsing function. I wonder how this number compares to Feferman's ϑ function, which, as you once stated, can take arguments of sort Ω_Ω_Ω... —Preceding unsigned comment added by LittlePeng9 (talk • contribs)

Definitions of \(\psi_0(\alpha)\) and \(\psi_1(\alpha)\) are also given by that subarticle. As for comparing \(\psi\) and \(\vartheta\) functions, I believe that the first one catches up the second at the Bachmann-Howard ordinal, since it is the first ordinal such that \(\vartheta(\Omega^\alpha) = \alpha\). Ikosarakt1 (talk ^ contribs) 20:55, March 30, 2013 (UTC)

Did I get the right ordinal? FB100Z • talk • contribs 16:58, April 4, 2013 (UTC)

Wait, no. FB100Z • talk • contribs 17:00, April 4, 2013 (UTC)

Is this also equal to \(\theta(\varepsilon_{\Omega_{\omega}+1},0)\)? DrCeasium (talk) 12:30, June 22, 2013 (UTC)

Yes, it is. Deedlit11 (talk) 09:58, July 2, 2013 (UTC)

Define the theta function (which I prefer over psi) for ordinals such as omega 2.BTD6 maker (talk) 16:37, August 22, 2014 (UTC)

Which theta? There's one defined here you're.so.pretty! 16:48, August 22, 2014 (UTC)

Note that the \(\psi\) function as defined by Rathjen (see for example Ordinal Notations IV on my blog) are more similar to the original \(\vartheta\) function rather than Pohler's original \(\psi\) function. Deedlit11 (talk) 02:30, August 24, 2014 (UTC)

CA[]

Forgive me for being dumb, but what does CA mean?, i only know BI is bar induction. thanks in advance!

(Chronolegends (talk) 23:17, September 3, 2016 (UTC))

IDK AarexWikia04 - 00:00, September 4, 2016 (UTC)

In subsystems of second-order arithmetic, CA stands for "comprehension axiom." That term isn't typically found on its own, and it usually takes on the form "foo-comprehension axiom," which is another way of saying "axiom schema of comprehension for formulas of type foo." So \(\Pi_1^1\)-\(\text{CA}\) means "\(\Pi_1^1\)-comprehension axiom." Importantly, the dash is not a minus sign. -- v e l! 09:15, September 4, 2016 (UTC)