# n-consistency - provability/truth of $\Sigma^0_n$ and $\Pi^0_{n+1}$ -formulas; n-consistent extensions, etc

I've been working through a textbook, often encountering difficulties with the exercises. On mathstackexchange, with most of them I haven't arrived yet at a satisfactory solution.

As I understand, they might be not ideally phrased, but I don't know what should be changed, or I don't see a good possibility to rewrite them. If you miss some background information, I will try to provide it.

If it would cost too much time, maybe you like to leave hints for (better/more detailed) solutions or general, short descriptions how the solution 'looks like'.

In future I'll try to write in a way that can more easily be answered. Of course nobody should feel forced to answer, in the past it seemed people sometimes feel that way, to my surprise.

https://math.stackexchange.com/questions/3039763/n-consistency-provability-truth-of-sigma0-n-and-pi0-n1-formulas-n

• Thanks for the link. I suggest you also include here the relevant definitions and question rather than having them only at the link. The idea is that, even if the other question disappears, this one should still make sense. Also, be explicit (not just "a textbook", but name, author, year, section, page, whatever else seems relevant). – Andrés E. Caicedo Dec 22 '18 at 15:28
• Related meta discussion: math.meta.stackexchange.com/questions/29498/… – Noah Schweber Dec 22 '18 at 19:15
• @AndrésE.Caicedo Thanks! Yeah I thought about just copy-paste the whole thing, but thought also that it would be more economic/practical to have the answers/discussions only on one site, so I only left the link. OK I'll change that in the future. – Ettore Dec 23 '18 at 8:47