Timeline for Is there an infinitary sentence which is absolutely not second-order expressible?
Current License: CC BY-SA 4.0
17 events
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| S Dec 6, 2021 at 22:30 | history | bounty ended | Noah Schweber | ||
| S Dec 6, 2021 at 22:30 | history | notice removed | Noah Schweber | ||
| Dec 3, 2021 at 20:41 | vote | accept | Noah Schweber | ||
| Dec 3, 2021 at 16:24 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| Dec 3, 2021 at 16:23 | comment | added | Noah Schweber | @FedorPakhomov Yes I forgot to include that - note that the restriction to infinite models shows up implicitly in my claim that "projective infinitary = second-order" (without an infinite domain to work with this doesn't hold). Fixed, thanks! | |
| Dec 3, 2021 at 12:46 | answer | added | Fedor Pakhomov | timeline score: 7 | |
| Dec 3, 2021 at 11:45 | comment | added | Fedor Pakhomov | The answer is no for fairly boring reason. Reasoning in $\mathsf{ZFC}+V=L$ consider some set $C$ of finite models in the signature of pure equality such that for no second-order sentence $\varphi$ we have $M\models \varphi\iff M \in C$ ($C$ exists by cardinality argument). Since validity of second-order sentences in finite models isn't changed by forcing any $\mathcal{L}_{\omega_1,\omega}$-formula $\psi$ axiomatizing $C$ gives a counterexample. I guess the right question should be about infinite models. | |
| Dec 2, 2021 at 21:13 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| Dec 2, 2021 at 20:51 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| S Dec 2, 2021 at 20:51 | history | bounty started | Noah Schweber | ||
| S Dec 2, 2021 at 20:51 | history | notice added | Noah Schweber | Draw attention | |
| S Oct 31, 2020 at 6:06 | history | bounty ended | CommunityBot | ||
| S Oct 31, 2020 at 6:06 | history | notice removed | CommunityBot | ||
| Oct 23, 2020 at 4:44 | history | edited | Noah Schweber | CC BY-SA 4.0 |
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| S Oct 23, 2020 at 4:17 | history | bounty started | Noah Schweber | ||
| S Oct 23, 2020 at 4:17 | history | notice added | Noah Schweber | Draw attention | |
| Oct 10, 2020 at 21:37 | history | asked | Noah Schweber | CC BY-SA 4.0 |