Timeline for Can we prove set theory is consistent?
Current License: CC BY-SA 2.5
4 events
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| May 2, 2010 at 18:16 | comment | added | Peter LeFanu Lumsdaine | Thanks! Yes, I think the difference in our answers is indeed coming from that — or more generally, from the fact that he's considering the case where we're letting the external theory be stronger than the internal one, whereas I'm looking at the case where the external theory is the same as the internal one or weaker. The former is perhaps more typical of informal practice (we don't want to limit the strength of our meta-theory; cf. Conway's "Mathematicians' Liberation Movement") while the latter is generally preferred in foundations/formalisation/metamathematics, I think. | |
| Apr 29, 2010 at 19:35 | comment | added | Andrea Ferretti | You answer is very interesting. I already accepted Carl's answer, which discusses another point of view. It seems to me that the answer is different whether we take set theory as given, and formalize logic inside it, or viceversa take logic as given and use it to build set theory. | |
| Apr 29, 2010 at 17:36 | history | edited | Peter LeFanu Lumsdaine | CC BY-SA 2.5 |
typo fixes, + made references to PA vs. HA more consistent
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| Apr 29, 2010 at 17:27 | history | answered | Peter LeFanu Lumsdaine | CC BY-SA 2.5 |