Timeline for What is the consistency strength of weak Vopenka's principle?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 22, 2019 at 20:55 | review | Close votes | |||
| Apr 23, 2019 at 5:20 | |||||
| Apr 22, 2019 at 13:43 | vote | accept | Tim Campion | ||
| Apr 21, 2019 at 20:06 | answer | added | Trevor Wilson | timeline score: 14 | |
| Aug 29, 2018 at 14:44 | comment | added | Tim Campion | The construction of an embedding $Ord \to C$ given above only works in certain $C$, such as the category of graphs, but that's fine. | |
| Aug 29, 2018 at 14:42 | comment | added | Tim Campion | @HarryGindi Not only is not every linear a well-order, but the morphisms of well-orderings are also much more restrictive than those of linear orders. For the statement, see Lemma 6.2 of Adamek-Rosicky. From a large discrete full subcategory $(A_i)_{i \in Ord} \subseteq C$, one constructs an embedding $Ord \to C$ by sending $i \mapsto \amalg_{j < i} A_j$. Conversely, an embedding $Ord \to C$ for $C$ locally presentable contradicts the form of Vopenka's principle which says that any class $(A_i)_{i \in Ord} \subseteq C$ admits a morphism $A_i \to A_j$ for some $i < j$. | |
| Aug 29, 2018 at 14:34 | vote | accept | Tim Campion | ||
| Apr 22, 2019 at 13:43 | |||||
| Aug 29, 2018 at 13:00 | comment | added | Alex Kruckman | @HarryGindi Not every linear order is a well-order. | |
| Aug 29, 2018 at 10:01 | comment | added | Harry Gindi | I am trying to recall this statement of VP (that ORD admits no full embedding in any locally presentable cat) and I can't find it. Isn't ORD the skeleton of LinOrdSet, though? | |
| Aug 29, 2018 at 8:55 | answer | added | Ivan Di Liberti | timeline score: 5 | |
| Aug 29, 2018 at 2:18 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Aug 29, 2018 at 1:58 | history | asked | Tim Campion | CC BY-SA 4.0 |