Timeline for Can one exhibit an explicit Kuratowski infinite set without invoking Replacement?
Current License: CC BY-SA 3.0
22 events
| when toggle format | what | by | license | comment | |
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| Aug 17, 2019 at 21:08 | vote | accept | Adam Epstein | ||
| Aug 5, 2019 at 18:55 | vote | accept | Adam Epstein | ||
| Aug 5, 2019 at 19:21 | |||||
| Jun 21, 2019 at 5:07 | answer | added | Elliot Glazer | timeline score: 9 | |
| S Aug 14, 2013 at 15:15 | history | suggested | Michael Albanese | CC BY-SA 3.0 |
Replaced \\, with \,.
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| Aug 14, 2013 at 15:07 | review | Suggested edits | |||
| S Aug 14, 2013 at 15:15 | |||||
| Jan 4, 2013 at 0:25 | comment | added | Theo Johnson-Freyd | This title is much better — thank you! | |
| Jan 3, 2013 at 23:40 | comment | added | Adam Epstein | @Goldstern See Kunen, Chapter IV Exercise (9) | |
| Jan 3, 2013 at 23:33 | history | edited | Adam Epstein | CC BY-SA 3.0 |
made the title more informative
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| Jan 3, 2013 at 13:36 | comment | added | Joel David Hamkins | ...and regarding Theo's suggestion, you could also add "Kuratowski infinite" to such a title, since an important point of the question is to replace the usual statement of Infinity with Kuratowski infinite. | |
| Jan 3, 2013 at 5:44 | comment | added | Theo Johnson-Freyd | This question seems to be a great one. (I say "seems to be" only because I am not an expert in set theory.) But I request that you modify the title. Titles on MO can be as long as text messages, and proper style is to include in your title a complete short version of your question. The current title, "Explicit Infinite Set", says very little about the question. You could instead use something like "In a version of ZF without Replacement, can an explicit infinite set be constructed from its implicit existence?" Or perhaps some variation better captures your question... | |
| Jan 2, 2013 at 22:56 | history | edited | Aaron Meyerowitz | CC BY-SA 3.0 |
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| Jan 2, 2013 at 22:48 | comment | added | Adam Epstein | Regarding Coret, he is not explicit about his formulation of the Axiom of Infinity. Perhaps none is needed - after all, if no infinite set exists then every set is hereditarily finite, though to deduce this in the sense as posted seemd to require Foundation. | |
| Jan 2, 2013 at 22:37 | history | edited | Zev Chonoles | CC BY-SA 3.0 |
deleted 19 characters in body; added 8 characters in body
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| Jan 2, 2013 at 22:35 | history | edited | Adam Epstein | CC BY-SA 3.0 |
added 2 characters in body
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| Jan 2, 2013 at 22:31 | comment | added | Goldstern | Can you motivate why you would be interested in such a system that appears to be too weak to prove the existence of certain very basic and natural objects? | |
| Jan 2, 2013 at 22:29 | history | edited | Zev Chonoles | CC BY-SA 3.0 |
improved LaTeX more
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| Jan 2, 2013 at 22:29 | history | edited | Adam Epstein | CC BY-SA 3.0 |
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| Jan 2, 2013 at 22:29 | history | edited | Goldstern | CC BY-SA 3.0 |
quotes
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| Jan 2, 2013 at 22:27 | comment | added | Goldstern | A natural definition for finiteness of $X$ (equivalent to the usual characterisation by natural numbers, without AC) is the one defined by Tarski: Every nonempty subset of the power set has a maximal element. | |
| Jan 2, 2013 at 22:25 | comment | added | Joel David Hamkins | Could you clarify what precisely the notion of finite is that you use in stating your axiom of Infinity? (You say "following Kuratowski", but I'm not sure exactly what you mean...) | |
| Jan 2, 2013 at 22:21 | history | edited | Adam Epstein | CC BY-SA 3.0 |
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| Jan 2, 2013 at 22:15 | history | asked | Adam Epstein | CC BY-SA 3.0 |