Timeline for Consistency of Nontrivial Elementary Embedding from $\omega_1$ to itself?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Aug 30, 2018 at 15:52 | comment | added | Thomas Benjamin | @Zetatopology: Are you interested in a nontrivial elementary embedding from $\omega_1$ into itself or of an $\omega_1$-model of $ZFC$ into itself? Please clarify. | |
| Aug 29, 2018 at 8:12 | history | edited | Emil Jeřábek | CC BY-SA 4.0 |
explain abbreviations
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| Aug 29, 2018 at 5:45 | comment | added | James E Hanson | Very little is actually first-order definable in ordinals as pure linear orders. I believe that $\omega^{\omega+1} = \omega^\omega \times \omega$ has $\omega^{\omega}\times \{0,2,3,4,\dots\}$ (i.e. delete the second $\omega^\omega$ block) as an isomorphic proper elementary substructure, which implies that for any ordinal $\alpha \geq \omega^{\omega+1}$ there's an explicit ZFC definable non-trivial elementary embedding of $\alpha$ into itself as a linear order. | |
| Aug 29, 2018 at 3:42 | comment | added | Keith Millar | How so @JamesHanson? | |
| Aug 28, 2018 at 22:43 | comment | added | James E Hanson | When you say elementary embedding of $\omega_1$ into itself what language are you talking about? If it's just $\omega_1$ as a linear order then I think there's an explicit ZFC definable non-trivial elementary embedding of it into itself. | |
| Aug 28, 2018 at 20:02 | history | edited | Zetapology | CC BY-SA 4.0 |
Axiom schema reduced to single axiom
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| Aug 28, 2018 at 18:10 | history | edited | Zetapology | CC BY-SA 4.0 |
Edited bad definitions
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| Aug 28, 2018 at 17:27 | history | edited | Wojowu | CC BY-SA 4.0 |
MathJax in the title
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| Aug 28, 2018 at 17:26 | comment | added | Monroe Eskew | It follows from $0^\sharp$. I would guess it’s equivalent. | |
| Aug 28, 2018 at 17:22 | comment | added | Wojowu | @EmilJeřábek FOST = the language of first-order set theory, IDK = I don't know | |
| Aug 28, 2018 at 17:15 | comment | added | Emil Jeřábek | What is FOST and IDK? | |
| Aug 28, 2018 at 17:10 | comment | added | Andreas Blass | Does your ZFC+CI include instances of replacement (or collection and separation) that involve the new symbol $j$, or only the instances in the original language of ZFC? | |
| Aug 28, 2018 at 16:31 | history | asked | Zetapology | CC BY-SA 4.0 |