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## Unsound ordinalsAdd to your list(s) Download to your calendar using vCal - A.R.D. Mathias
- Monday 13 May 2013, 11:00-12:00
- MR13.
If you have a question about this talk, please contact ok261. An ordinal zeta is Woodin in 1982 raised the question whether unsound ordinals ordinals exist; the answer I found then (to be found in a paper published in 1984 in Math Proc Cam Phil Soc) is this: Assume DC. Then the following are equivalent: i) the ordinal $\omega_1^{\omega + 2}$ (ordinal exponentiation) is unsound ii) there is an uncountable well-ordered set of reals That implies that if omega_1 is regular and the ordinal mentioned in i) is sound, then omega_1 is strongly inaccessible in the constructible universe. Under DC, every ordinal strictly less than the ordinal mentioned in i) is sound. There are many open questions in this area: in particular, in Solovay’s famous model where all sets of reals are Lebesgue measurable, is every ordinal sound ? The question may be delicate, as Kechris and Woodin have shown that if the Axiom of Determinacy is true then there is an unsound ordinal less than omega_2. This talk is part of the ok261's list series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
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