Timeline for Z_2 versus second-order PA
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| May 18, 2012 at 4:13 | comment | added | David Roberts♦ | I know $ATR_0$ proves the consistency of $ACA_0$, I didn't know it proves the consistency of $ACA$. | |
| May 18, 2012 at 2:36 | history | edited | Ali Enayat | CC BY-SA 3.0 |
added 76 characters in body
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| May 16, 2012 at 11:09 | comment | added | Ali Enayat | @David: In my answer to question 2, I mentioned $PA$ in order to highlight the fact that for the same Godelian reasons that $PA$ is weaker than $ACA$, $ACA$ is in turn weaker than $Z_2$. @Carl, $ACA$, being an axiomatizable theory, has many non-$\omega$ models, so your model-theoretic argument for conservativity will not work for such models. | |
| May 16, 2012 at 3:30 | comment | added | David Roberts♦ | "Regarding the second question..." I was asking about $PA_2$ :-) I know $PA$ is weaker than $ACA$. | |
| May 16, 2012 at 3:18 | history | answered | Ali Enayat | CC BY-SA 3.0 |