Timeline for Proper classes subnumerous to $V$ in a model of a Morse-Kelley related theory
Current License: CC BY-SA 3.0
38 events
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| Dec 28, 2021 at 19:54 | vote | accept | Zuhair Al-Johar | ||
| Sep 23, 2016 at 15:34 | answer | added | Zuhair Al-Johar | timeline score: 1 | |
| Sep 21, 2016 at 12:52 | answer | added | Zuhair Al-Johar | timeline score: -1 | |
| Sep 21, 2016 at 12:20 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
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| Sep 20, 2016 at 20:30 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
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| Sep 20, 2016 at 20:25 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
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| Sep 20, 2016 at 20:19 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
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| Sep 20, 2016 at 17:34 | comment | added | Joel David Hamkins | In general, the operation of removing an axiom from a theory is not well-defined up to logical equivalence. An interesting case is the removal of the power set axiom from ZFC: jdh.hamkins.org/what-is-the-theory-zfc-without-power-set | |
| Sep 20, 2016 at 16:19 | comment | added | Joel David Hamkins | Could you state clearly the axioms that are in your theory, rather than which are not? There are several different equivalent formulations of Kelley-Morse, and some of them, for example, do not use the so-called Limitation of size axiom. | |
| Sep 20, 2016 at 16:00 | answer | added | Noah Schweber | timeline score: 3 | |
| Sep 20, 2016 at 15:56 | history | reopened |
R.P. David White Michael Albanese Emil Jeřábek Noah Schweber |
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| Sep 20, 2016 at 13:51 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
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| Sep 19, 2016 at 17:13 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
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| Sep 19, 2016 at 17:06 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
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| Sep 19, 2016 at 17:00 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
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| Sep 19, 2016 at 16:54 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
Claim specifically clarified, general context explained, comments addressed and special contexts been raised.
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| Sep 18, 2016 at 21:54 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
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| Sep 18, 2016 at 21:48 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
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| Sep 16, 2016 at 8:17 | review | Reopen votes | |||
| Sep 16, 2016 at 17:09 | |||||
| Sep 16, 2016 at 8:17 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
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| Sep 16, 2016 at 8:11 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
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| Sep 16, 2016 at 8:01 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
the claim is putting in formulas to avoid confusion, and addition question was posed to expand on the subject.
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| Sep 16, 2016 at 5:21 | history | closed |
Andrés E. Caicedo Jan-Christoph Schlage-Puchta Stefan Kohl♦ Wolfgang user1688 |
Needs details or clarity | |
| Sep 16, 2016 at 4:50 | comment | added | Zuhair Al-Johar | to avoid confusion rising from the last line in my latest comment, I meant .. the question is if that is "possible" for all such proper classes, I meant if it is consistent to have that. | |
| Sep 15, 2016 at 19:18 | comment | added | Zuhair Al-Johar | Yes the additional property I've added it to the question, that the model must have a proper class that is strictly subnumerous to V, so given that condition non of the models of the traditional version of KM that proves global choice is a model that I'm asking about. As regards your last question, I'm asking about the 'size' of a proper class and not its set-hood, yes a proper class is not a set, but it can be equi-numerous to a set? you don't have Replacement axiomatized here! the question is if that can be true of all proper classes that are strictly subnumerous to V. | |
| Sep 15, 2016 at 15:56 | comment | added | Joel David Hamkins | I'm still a little confused about what you want. If there is a proper class that is smaller than $V$, then by the meaning of "proper" class, it is not a set. | |
| S Sep 15, 2016 at 15:24 | history | suggested | user642796 | CC BY-SA 3.0 |
More descriptive title; some formatting; added a "top-level" tag
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| Sep 15, 2016 at 14:59 | review | Suggested edits | |||
| S Sep 15, 2016 at 15:24 | |||||
| Sep 15, 2016 at 13:39 | comment | added | Joel David Hamkins | My point is that every model of KM itself is also a model of that weak fragment, since nothing in your theory prevents this. I guess you intended to ask for a model with some additional properties, such as not having global choice etc.? | |
| Sep 15, 2016 at 13:19 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
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| Sep 15, 2016 at 13:16 | comment | added | Zuhair Al-Johar | The theory I'm speaking about is not MK, it is a weak fragment of MK in which the axiom of subsets replace the axiom of limitation of size, also you don't have the union axiom, this theory doesn't prove global choice, so some models of it does have proper classes that are strictly smaller than V, for example you can have a model in which Ord is strictly subnumerous to V. Can you have such a model in which all of such classes are of set size? | |
| Sep 15, 2016 at 12:22 | comment | added | Joel David Hamkins | Could you clarify the question? Any model of KM itself has a bijection of V with Ord by the global choice axiom, and so any class that is strictly smaller than V is in fact bijective with an ordinal and hence is a set. So the property seems to be true (vacuously) in any model of KM, without needing to remove any axioms at all. | |
| Sep 15, 2016 at 11:36 | review | Close votes | |||
| Sep 16, 2016 at 5:21 | |||||
| Sep 15, 2016 at 9:43 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
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| Sep 15, 2016 at 9:38 | history | undeleted | Zuhair Al-Johar | ||
| Sep 15, 2016 at 9:31 | history | deleted | Zuhair Al-Johar | via Vote | |
| Sep 15, 2016 at 9:25 | history | edited | Zuhair Al-Johar | CC BY-SA 3.0 |
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| Sep 15, 2016 at 9:14 | history | asked | Zuhair Al-Johar | CC BY-SA 3.0 |