Timeline for About the notions of Grothendieck Universe and Tarski Universe
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 5, 2012 at 7:11 | history | edited | Charles Matthews | CC BY-SA 3.0 |
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| Jul 5, 2012 at 5:34 | comment | added | Buschi Sergio | Sorry for ENglish, but I write above: "...Then by these premises...", I mean that (1), (2), (3) are premises. THen If $U$ has the properties (1), (2), (3) , how can I prove that $(4)\Leftrightarrow (4')$? | |
| Jul 5, 2012 at 5:29 | comment | added | Buschi Sergio | David ROberts: From $|U|\subset U$ if $|x|<|U|$ i.e. $|x|\in |U|$ follow $|x|\in U$ and from (4') follow $x\in U$. | |
| Jul 5, 2012 at 4:27 | comment | added | Andreas Blass | A simpler counterexample to (4) and (4') is $V_{\omega+\omega}$. But the question is not to infer (4) and/or (4') from (1,2,3) but rather to infer that (4) is equivalent to (4'). | |
| Jul 5, 2012 at 2:40 | answer | added | Andreas Blass | timeline score: 5 | |
| Jul 5, 2012 at 2:25 | comment | added | Noah Schweber | This also provides a counterexample to 4'. | |
| Jul 5, 2012 at 2:24 | comment | added | Noah Schweber | Property 4 appears not to follow. Assume GCH; then $U:=V_{\aleph_\omega}$ satisfies (1)-(3), but the set $\{\aleph_n: n\in\omega\}$ is a set with cardinality $<\vert U\vert$ but not in $U$. Is there more to the exercise? | |
| Jul 4, 2012 at 23:45 | comment | added | David Roberts♦ | Why are you trying to prove $|U| \subset U$? | |
| Jul 4, 2012 at 22:06 | history | asked | Buschi Sergio | CC BY-SA 3.0 |