Timeline for How dangerous are set-size assumptions?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jun 22, 2019 at 9:05 | comment | added | Monroe Eskew | Whoever is downvoting should explain what is wrong with what I said. I would like to know. | |
| Jun 21, 2019 at 11:47 | history | edited | Monroe Eskew | CC BY-SA 4.0 |
added 793 characters in body
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| Jun 21, 2019 at 10:49 | comment | added | user44143 | Indeed. So it would help to clarify the answer. | |
| Jun 21, 2019 at 4:51 | comment | added | Monroe Eskew | @MattF. But it’s not. The former proves Con(ZFC). | |
| Jun 20, 2019 at 21:35 | comment | added | user44143 | There is a standard way to say that! "ZFC + Universes is conservative over ZFC for arithmetical statements." | |
| Jun 20, 2019 at 20:35 | comment | added | Monroe Eskew | @MattF. I meant to allow more general examples like for example comparing mutually inconsistent theories in a “standard interpretation” hierarchy. For example comparing $ZFC$ to $ZFC^- +$ “There are exactly 3 infinite cardinals.” I want to say their arithmetical theories are compatible while their general theories need not be. | |
| Jun 20, 2019 at 6:06 | comment | added | Monroe Eskew | @PaceNielsen well it proves all of the statements you mention... | |
| Jun 20, 2019 at 0:39 | comment | added | Pace Nielsen | I think by "safe" I mean not just consistent with PA, but consistent with all arithmetic true we would naturally accept. This would include Con(PA) as well as Con(PA+Con(PA)), etc... It might also include deeper things like Goodstein's theorem. | |
| Jun 19, 2019 at 22:26 | history | answered | Monroe Eskew | CC BY-SA 4.0 |