Timeline for Examples of statements that are valid in every spatial topos
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 26, 2022 at 9:41 | comment | added | მამუკა ჯიბლაძე | Booleanness implies AC for localic toposes (if your set theory has it, that is), but not for non-localic Grothendieck toposes. Do such examples count? | |
| Nov 26, 2022 at 3:41 | answer | added | Ingo Blechschmidt | timeline score: 12 | |
| Jun 10, 2022 at 14:23 | comment | added | Zhen Lin | Yes, infinite disjunctions, and infinitely many axioms. | |
| Jun 10, 2022 at 12:28 | comment | added | Gro-Tsen | @ZhenLin: To be sure I understand, you need infinite conjunctions or disjunctions to express such theories, right? | |
| Jun 10, 2022 at 11:39 | comment | added | Zhen Lin | Anyway, back to your original question: how about theories in geometric logic? There are many examples of propositional theories that have no models in any spatial topos but do have models in some localic toposes. (Every locale without points gives rise to such a thing, tautologically!) | |
| Jun 10, 2022 at 11:33 | comment | added | Zhen Lin | @Gro-Tsen Actually I think even the joke compromise is conventionally the other way around: "Grothendieck topoi" but "elementary toposes". | |
| Jun 10, 2022 at 6:56 | history | edited | Gro-Tsen | CC BY-SA 4.0 |
clarify that I'm asking about questions in the internal language (thereby also making sure that "internal language" appears in the text so it can be searched)
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| Jun 9, 2022 at 20:45 | comment | added | Gro-Tsen | @AlexKruckman: I admit I don't remember where I got this, and it's a bit of a joke compromise, but the logic is that it's not the same word: Grothendieck forged “un topos” as a companion to “une topologie” (and he and his students used “des topos” as plural), whereas Lawvere thought of the Greek word “τόπος”. | |
| Jun 9, 2022 at 19:58 | comment | added | Alex Kruckman | Footnote 2 made me laugh. What is the source of this convention?? | |
| Jun 9, 2022 at 18:15 | comment | added | Maxime Ramzi | I'm not sure but I think the fact that any Grothendieck topos admits a (geometric) surjection from a localic topos might be relevant to the second separation | |
| Jun 9, 2022 at 16:39 | history | asked | Gro-Tsen | CC BY-SA 4.0 |