Timeline for In the construction of $K^c$ for sequences of measures, why do we only add measures of cofinality $\omega_1$?
Current License: CC BY-SA 4.0
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| Jul 21 at 15:27 | comment | added | Gabe Goldberg | I don't know, it's been 10 years since I read Zeman's book. Steel makes a similar move when he defines $K^c$ in The Core Model Iterability Problem; look at the conditions for adding an extender to the $K^c$ sequence (Case 1 on page 6). Again, this is to ensure that there is a thick set of ordinals that are not measurable; look at property (iv) on page 9. In the end, $K^c$ is constructed in order to extract $K$, so I guess the certification it is a matter of convention as long as it does not affect $K$. | |
| Jul 21 at 2:47 | comment | added | Connor W | @GabeGoldberg Thanks for your reply, Gabe. As a follow-up question, is there a reason this is not done in Zeman's book? Is it a matter of convention whether or not $K^c$ only has measurables of cofinality $\omega_1$? | |
| Jul 20 at 22:14 | comment | added | Gabe Goldberg | Mitchell wants the class of fixed points of an iteration of $K^c$ to be thick; see Proposition 4.8. | |
| Jul 20 at 1:26 | history | edited | Connor W | CC BY-SA 4.0 |
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| Jul 19 at 19:46 | history | asked | Connor W | CC BY-SA 4.0 |