Timeline for Star-transfer of powerset
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 1, 2015 at 1:30 | comment | added | Riley | I finally got a chance to read Robinson's book. Now this makes complete sense to me. Thanks so much! | |
| Sep 1, 2015 at 1:29 | vote | accept | Riley | ||
| Nov 25, 2012 at 2:29 | comment | added | Joel David Hamkins | Asaf, the situation is that we have the standard universe $V$, which can see everything, and then the transfer principle map $j:V\to {}^\ast V$, which is an elementary embedding. Since $V$ sees this map and all of ${}^\ast V$, it has ${}^\ast\mathbb{R}$ and all its subsets, but the nonstandard universe ${}^\ast V$ only has the subsets that are visible in that universe. With this notation, what we have is ${}^\sigma\cal{P}(\mathbb{R})=j''\cal{P}(\mathbb{R})$, ${}^\ast\cal{P}(\mathbb{R})=j(\cal{P}(\mathbb{R}))$ and ${\cal{P}}({}^\ast\mathbb{R})=P(j(\mathbb{R}))^V$. | |
| Nov 24, 2012 at 23:20 | comment | added | Joel David Hamkins | They do exist in the standard universe, since they are standard subsets of ${}^\ast\mathbb{R}$, but they do not exist in the non-standard universe, since they would reveal to that universe that the reals are incomplete or non-Archimedean. | |
| Nov 24, 2012 at 23:15 | comment | added | Asaf Karagila♦ | The last sentence of the first point should perhaps end with "these particular subsets do not exist in the standard universe." or am I missing something? | |
| Nov 24, 2012 at 23:09 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 177 characters in body; added 7 characters in body; deleted 1 characters in body; added 35 characters in body
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| Nov 24, 2012 at 22:36 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |