Timeline for From elementary equivalence to isomorphism
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 27, 2013 at 23:00 | comment | added | Joseph Van Name | Saturated structures of the same cardinality are isomorphic. More generally, special structures of the same cardinality are isomorphic. Also, any pair of homogeneous structures of the same cardinality that realize the same $n$-types are isomorphic. Here a structure $A$ is said to be homogeneous if whenever $\lambda<|A|$, and the structures $(A,(a_{\alpha})_{\alpha<\lambda}),(A,(b_{\alpha})_{\alpha<\lambda})$ are elementarily equivalent, then for each $a\in A$ there is a $b\in B$ where $(A,(a_{\alpha})_{\alpha<\lambda},a),(A,(b_{\alpha})_{\alpha<\lambda},b)$ are elementarily equivalent. | |
| Nov 27, 2013 at 19:14 | review | Close votes | |||
| Nov 27, 2013 at 21:17 | |||||
| Nov 27, 2013 at 19:07 | answer | added | Will | timeline score: 2 | |
| Nov 27, 2013 at 17:19 | comment | added | Benjamin Steinberg | It happens for finite structures :) | |
| Nov 27, 2013 at 16:59 | comment | added | Asaf Karagila♦ | This happens if and only if whenever $\operatorname{Th}(M)=\{\varphi\mid M\models\varphi\}$ is a $\kappa$-categorical theory, where $|M|=\kappa$. | |
| Nov 27, 2013 at 16:50 | history | asked | Quercus | CC BY-SA 3.0 |