Timeline for Inner model in which every uncountable cardinal is large

7 events

when toggle format	what		by	license	comment
Apr 22, 2014 at 16:15	comment	added	Rachid Atmai		No, $L(\mathbb{R})$ does not satisfy $AC$. It will however satisfy definable uniformization principles and the "Coding Lemma", which is a choice principle. In general $L(A)$ satisfies choice only if $A \subset L$.
Apr 22, 2014 at 9:10	comment	added	Mohammad Golshani		Does $L(\mathbb{R})$ satisfy $AC$ in this case?
Apr 21, 2014 at 20:48	comment	added	Rachid Atmai		Sorry, I meant $\mathcal{M}_{\omega}^{\sharp}$ in the previous comment instead of $\mathcal{M}_{n}^{\sharp}$ .
Apr 21, 2014 at 20:08	comment	added	Rachid Atmai		A weaker result than what you're specifically looking for is that assuming that there are $\omega$ many Woodin cardinals and a measurable above them (i.e $\mathcal{M}_n^{\sharp}$), then every regular cardinal in $L(\mathbb{R})$ is measurable. This is a theorem of Steel.
Apr 21, 2014 at 14:42	vote	accept	Mohammad Golshani
Apr 21, 2014 at 7:37	answer	added	Philip Welch		timeline score: 11
Apr 21, 2014 at 5:27	history	asked	Mohammad Golshani	CC BY-SA 3.0