Difference between revisions of "Userblog:Julian Barathieu/Ordinal analyses"
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Revision as of 06:46, 12 February 2018
Currently in construction. Do not edit.
Contents
Arithmetical theories
Set theories
Ordinalcollapsing functions
Table of prooftheoretic ordinals and their corresponding theories
Prooftheoretic ordinal  Arithmetical theories  Set theories  References  Ordinal name 

$\varepsilon_0$  $ACA_0$  $KP\setminus Inf$  Epsilon zero  
$\psi_0(\varepsilon_{\Omega+1})$  $ACA+BI$  $KP$  [1]  BachmannHoward ordinal 
$\psi_0(\Omega_\omega)$  $\Pi^1_1CA_0, \Delta^1_2CA_0$  [2]  
$\psi_0(\Omega_\omega\epsilon_0)$  $\Pi^1_1CA$  [3]  
$\psi_0(\varepsilon_{\Omega_\omega+1})$  $\Pi^1_1CA+BI$  [4]  TakeutiFefermanBuchholz ordinal  
$\psi_0(\Omega_{\varepsilon_0})$  $\Delta^1_2CA$  [5] 
 $\text{ACA}_0 + $ Kruskal's Tree Theorem (full analysis), $\text{ACA}_0 + \Pi^1_n\text{BI}$ (full analysis):
https://www1.maths.leeds.ac.uk/~rathjen/KRUSKAL.neu.pdf
 Fragments of KP (restricted foundation) (full analysis): [6]
 $\text{KPi}$, $\Delta^1_2\text{CA+BI}$ (full cut elimination): [7]
 $\text{KPM}$ (full analysis): [8], [9]
 $\Delta^1_2\text{CA+BI +}$ parameterfree $\Pi^1_2\text{CA}$ (full analysis): [10]
 $\text{KP +}$ strong reflection principles (full analysis): [11]
 $\text{Stability}, \text{KP +}$ "for all $\alpha$, there is a $\alpha$stable ordinal " (full analysis): [12], [13]
 $\Pi^1_2\text{CA}_0, \Pi^1_2\text{CA+BI}, \Delta^1\_3\text{CA}$: [14]
 $\text{KP + V=L +}$ "there is an uncountable regular cardinal" (full cut elimination): [15]
https://www1.maths.leeds.ac.uk/~rathjen/Seppchiemsee.pdf  Pi^1\_1CA0, ID<w, Pi^1\_1CA  Pi^1\_1CA+BI, IDw, Delta^1\_2CR  Delta^1\_2CA, Delta^1\_2CA+BI = KPi