Timeline for Is there an abstract logic that defines the mantle?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| S Sep 24, 2023 at 9:52 | history | suggested | The Amplitwist | CC BY-SA 4.0 |
replaced proxy link with direct link to bookstore.ams.org
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| Sep 23, 2023 at 15:14 | review | Suggested edits | |||
| S Sep 24, 2023 at 9:52 | |||||
| Jul 27, 2020 at 20:30 | answer | added | Hanul Jeon | timeline score: 3 | |
| S Jul 27, 2020 at 10:35 | history | suggested | Later |
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| Jul 27, 2020 at 10:10 | review | Suggested edits | |||
| S Jul 27, 2020 at 10:35 | |||||
| Jul 27, 2020 at 9:12 | comment | added | Hanul Jeon | @GabeGoldberg Your argument seems relevant to Hamkins' previous answer. | |
| Jul 27, 2020 at 4:28 | comment | added | Gabe Goldberg | What if $\mathcal L$ has formulas $\varphi_x$ for every $x\in M$ such that $\varphi_x$ is false unless $\mathfrak{A}$ is a structure with one relation symbol and for some transitive $y\in M$, there is an isomorphism $f : \mathfrak{A}\to (y,\in)$ such that $f(x)\in y$. In other words, $\mathcal L$ has formulas coding all elements of $M$. It seems like by induction, the $\alpha$-th level of the $C(\mathcal L)$-hierarchy is $(V_\alpha)^M$. I worry that I am misunderstanding the definition of an abstract logic. | |
| Jul 27, 2020 at 2:21 | comment | added | Hanul Jeon | @GabeGolsberg Thank you for your comment. I did not know that it has an ambiguous definition (I initially assumed the definition in Model Theory by Chang and Keisler.) | |
| Jul 26, 2020 at 22:09 | comment | added | Gabe Goldberg | Can you be more specific about what you mean by an abstract logic? It is hard to find the definition online, or more accurately, it is easy to find a number of inequivalent definitions. It seems to me it might be possible to realize any inner model $M$ as $C(\mathcal L)$ for some proper class abstract logic $\mathcal L$ which is ad hoc yet definable from the predicate $M$. | |
| Jul 25, 2020 at 0:04 | comment | added | Jason Zesheng Chen | An observation: if the mantle has the form $L[A]$, where $A$ is a class of ordinals, then we may define an artificial $A$-recovering quantifier $Q^A$ as follows: $N\vDash (Q^A xy)\varphi(x,y,\vec{a})$ iff $\{(x,y)\in N^2\mid N\vDash \varphi(x,y,\vec{a})\}$ is a linear order of ordertype in $A$. Then the resulting model is just $L[A]$. | |
| Jul 24, 2020 at 21:49 | history | edited | Hanul Jeon | CC BY-SA 4.0 |
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| Jul 24, 2020 at 21:34 | history | edited | LSpice | CC BY-SA 4.0 |
Names of papers; link to Chang's paper
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| Jul 24, 2020 at 20:37 | history | edited | Hanul Jeon | CC BY-SA 4.0 |
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| Jul 24, 2020 at 20:31 | history | asked | Hanul Jeon | CC BY-SA 4.0 |