Timeline for The universe of sets, existential quantification in set theory
Current License: CC BY-SA 3.0
19 events
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| Mar 21, 2016 at 22:44 | answer | added | Thomas Benjamin | timeline score: 0 | |
| Mar 16, 2016 at 23:03 | comment | added | Thomas Benjamin | To all...it might help to read Dr. Fontanella's slide presentation, "On the definitional character of axioms", to understand the import of her question (and to understand why she asked it--this presentation is available on her homepage under "Talks"). It touches on topics presented in her question. | |
| Mar 16, 2016 at 9:54 | history | edited | Mikhail Katz | CC BY-SA 3.0 |
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| Mar 16, 2016 at 9:06 | answer | added | Thomas Klimpel | timeline score: 0 | |
| Mar 4, 2016 at 16:32 | answer | added | Andreas Blass | timeline score: 8 | |
| Mar 4, 2016 at 16:19 | history | reopened |
Joel David Hamkins Joonas Ilmavirta Wolfgang Asaf Karagila♦ Andreas Blass |
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| Mar 4, 2016 at 16:12 | comment | added | Nik Weaver | Are you essentially asking whether most mathematicians consider proper classes to be "objects" which are just as "real" as sets? I suspect that most people may not have a really well thought out opinion on the question. (Or even the question, in what sense are sets "real objects".) | |
| Mar 4, 2016 at 15:40 | history | edited | Laura Fontanella | CC BY-SA 3.0 |
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| Mar 4, 2016 at 14:31 | history | edited | Laura Fontanella | CC BY-SA 3.0 |
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| Mar 4, 2016 at 13:38 | review | Reopen votes | |||
| Mar 4, 2016 at 16:22 | |||||
| Mar 4, 2016 at 13:19 | history | edited | Laura Fontanella | CC BY-SA 3.0 |
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| Mar 4, 2016 at 10:19 | comment | added | Laura Fontanella | I understand your perplexities, so I should better explain my motivations. As a set theorist, I know the meaning of this statement and how one proves it from ZF, but I'm interested in how my colleagues interpret it, like a poll. For instance, Joel used the expressions "there is no set of all sets" and "there is no universal set", another way to read it is "the class of all sets is not a set". I believe that each of those expressions hides different philosophical standpoints, so I'm interested in what is your favorite interpretation. If that's an inappropriate use of MO, I apologise. | |
| Mar 3, 2016 at 15:56 | comment | added | Joel David Hamkins | In plain language, the assertion expresses: there is no set of all sets. That is, there is no set $x$ for which every set $y$ is a member of $x$. This is easy to prove in ZF, for if there were such a universal set $x$, then by the separation axiom the collection $z=\{ y\in x\mid y\notin y\}$ would also exist as a set, and in this case, since $z\in x$, we would have $z\in z$ just in case $z\notin z$, which is a contradiction. So there can be no universal set. This argument is fundamentally related to the Russell paradox. | |
| Mar 3, 2016 at 14:00 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Mar 3, 2016 at 14:00 | comment | added | Todd Trimble | Welcome to MO, Dr. Fontanella (on assumption this is your page: logique.jussieu.fr/~fontanella). Please excuse what may seem a summary dismissal of your question. A number of users flagged the question as one unlikely to be asked by a professional mathematician, so there's a good chance it was received differently from how you intended it. The question can be reopened, but I suggest (in keeping with site norms) that some further explanation/context/motivation be provided, to make clearer what you are intending. I'm also making this Community Wiki because many answers are possible. | |
| Mar 3, 2016 at 13:29 | history | closed |
Emil Jeřábek Andrés E. Caicedo Todd Trimble |
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| Mar 3, 2016 at 12:04 | review | Close votes | |||
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| Mar 3, 2016 at 11:39 | review | First posts | |||
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| Mar 3, 2016 at 11:30 | history | asked | Laura Fontanella | CC BY-SA 3.0 |