Timeline for What "forces" us to accept large cardinal axioms?
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| Dec 11, 2014 at 18:37 | comment | added | Timothy Chow | @JesseElliott : Usually what is needed is 1-consistency. If you think about it, there's no way that a large cardinal could be required by an arithmetical statement S in the strongest possible sense that its existence is actually implied by S, because there are models of true arithmetic in which there is no inaccessible cardinal. | |
| Dec 11, 2014 at 12:28 | comment | added | Jesse Elliott | In Friedman's examples, do you know if the consistency of a given large cardinal axiom enough to prove the given $\Pi^0_1$ statements, or does it actually require the existence of a given large cardinal? | |
| Apr 25, 2014 at 14:42 | history | answered | Timothy Chow | CC BY-SA 3.0 |