Timeline for Can FPA really prove its consistency?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| May 12, 2021 at 14:51 | comment | added | abo | This doesn't answer the question, but is related. It is possible to construct a system which "really proves" its consistency, by using functions rather than relationships as the second sort. In this case there is only one function, rather than two relationships, in the case where the set of first-sort elements = {0}, and so the proof of consistency is easier if not trivial. See researchgate.net/publication/… | |
| Feb 22, 2019 at 14:54 | answer | added | abo | timeline score: 0 | |
| Jan 23, 2019 at 16:44 | comment | added | abo | @Qfwfq. No, it is not needed. If you prefer, all elements of the domain can be natural numbers. | |
| Jan 23, 2019 at 13:58 | comment | added | Qfwfq | Just a naive question: is the $1$-ary relation $N$ really needed? | |
| Jan 23, 2019 at 9:21 | answer | added | abo | timeline score: 5 | |
| Jan 18, 2019 at 6:48 | comment | added | abo | Would anyone like to vet a proof that FPA (so $I \Delta_0 + \Omega_1$) can prove the consistency of $G$? The proof is unfortunately completely straightforward, so could well have an obvious (except to me) error in it. The system used is the one in Cook and Nguyen, excepting that the target formula of $\forall$-Left and $\exists$-Right is restricted to $\top$ or $\bot$. I've got the proof down to just less than 30000 characters, so could post it as an answer... Thanks very much... | |
| Jan 29, 2013 at 19:13 | vote | accept | abo | ||
| Jan 29, 2013 at 15:12 | comment | added | user21349 | @Amit Kumar Gupta: FPA omits PA2. | |
| Jan 29, 2013 at 14:18 | answer | added | Emil Jeřábek | timeline score: 20 | |
| Jan 29, 2013 at 9:11 | comment | added | Amit Kumar Gupta | What do you mean one cannot prove there exists $n$ such that $one(n)$? (PA2) with $n=0$, together with (PA1), gives precisely $\exists m \mathrm{one}(m)$. | |
| Jan 28, 2013 at 22:03 | history | asked | abo | CC BY-SA 3.0 |