Timeline for A question on ultrapower
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Feb 11, 2010 at 1:54 | comment | added | Joel David Hamkins | I have posted a revised answer, for the case mu_1 not in ran(j_01). Here, the answer is affirmative. | |
| Feb 11, 2010 at 0:17 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
Revised answer for case mu_1 not in ran(j_01).
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| Feb 6, 2010 at 2:08 | vote | accept | Ant emyy Lee | ||
| Feb 5, 2010 at 10:03 | vote | accept | Ant emyy Lee | ||
| Feb 5, 2010 at 10:03 | |||||
| Feb 5, 2010 at 10:02 | vote | accept | Ant emyy Lee | ||
| Feb 5, 2010 at 10:02 | |||||
| Feb 3, 2010 at 13:38 | comment | added | Joel David Hamkins | Welcome to MO! Ah, I read your question more carefully now. You are right: my answer applies to the case where mu_1 IS in the range of j_01, for then mu_1=j_01(nu), and in this case, j02 is precisely the ultrapower by mu_0 x nu, since every object in M_2 would be j02(f)(kappa_0,kappa_1), and you map this to [f]_{mu_0xnu} for an isomorphism. For your case, where mu_1 is NOT in the range of j_01, then I believe the answer is Yes, but this is more complicated, and I will post an answer later. | |
| Feb 3, 2010 at 3:20 | comment | added | Ant emyy Lee | So the model-theoretic fact you said in your answer may not make sense in this case, since $\mu_1$ is not a normal measure in $V$. How to deal with this case? | |
| Feb 3, 2010 at 3:20 | comment | added | Ant emyy Lee | I am the student exchange you with email, you introduce me to go here, so I register this new name. In my question, I require $\mu_1$ is not in the range of $j_{0,1}$, i.e. the second step of the iterated ultrapower is done by a normal measure not in $j_{0,1}''V$. For example, suppose $\kappa$ has $\kappa$ many normal measures <U_\alpha:\alpha<\kappa>, the first step of the iterated ultrapower I use $U_0$, and the second step of the iteration, I use the \kappa-th measure in the sequence j_{0,1}(<U_\alpha:\alpha<\kappa>) . | |
| Feb 2, 2010 at 5:14 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |