Timeline for On a weak choice principle
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Aug 7, 2020 at 0:43 | history | edited | François G. Dorais | CC BY-SA 4.0 |
fixed link
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| Aug 7, 2020 at 0:29 | history | edited | François G. Dorais | CC BY-SA 4.0 |
fixed grammar since question was bumped
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| Dec 14, 2017 at 6:24 | comment | added | David Roberts♦ | I've accepted this answer because it was most useful when formulating internal WISC in a topos, and so allowed me to carry out Mike's suggestion in his answer in a stronger way, and violate internal WISC, not just external, which is immediate. | |
| Dec 14, 2017 at 6:22 | vote | accept | David Roberts♦ | ||
| Jun 19, 2012 at 1:35 | comment | added | David Roberts♦ | Hmm, this variant (exists a $C$ and a collection of surjections $C \to X$) is just a bit weaker than COSHEP, and should be interesting on its own in settings other than a well-pointed Boolean topos. | |
| Jun 18, 2012 at 23:42 | history | edited | François G. Dorais | CC BY-SA 3.0 |
small cleanup; added 15 characters in body
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| Jun 18, 2012 at 21:13 | comment | added | François G. Dorais | Another translation detail... Benno's literal construction would require that trees $T$ in $\mathcal{W}$ are also cleanly branching in the sense that $\lbrace x \in C : t^\frown x \in T \rbrace$ is either $\varnothing$ (label $0$) or all of $C$ (any label $i \in I$). Since it makes no difference in the argument, I did not include that restriction. | |
| Jun 18, 2012 at 20:58 | history | edited | François G. Dorais | CC BY-SA 3.0 |
addendum
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| Jun 18, 2012 at 20:40 | comment | added | François G. Dorais | I'll add the argument why the $C_i$'s can all be the same in a minute. I simplified Benno's argument a bit. The labels are not necessary since I'm using subtrees of $C^{<\omega}$. I also removed the extra label $1$ since the usual rank function also takes care of successor ordinals. | |
| Jun 18, 2012 at 20:26 | comment | added | Andreas Blass | Francois, maybe I'm just being dense today, but I don't see why you can assume that all the $C_i$ are the same set $C$. And I don't see anything about that in Benno's write-up either; insofar as I understand W-types, he seems to be using trees in which the nodes are labeled by elements of the index set $I$. | |
| Jun 18, 2012 at 18:56 | history | answered | François G. Dorais | CC BY-SA 3.0 |