Timeline for Real closed fields in HOD

6 events

when toggle format	what		by	license	comment
Dec 18, 2013 at 8:07	vote	accept	user38200
Dec 12, 2013 at 17:38	comment	added	Andreas Blass		@EmilJeřábek Thanks for adding that clarification; I guess I should have included it in my comment.
Dec 12, 2013 at 13:12	comment	added	Emil Jeřábek		To avoid confusion, it can only be larger than $\mathfrak c^{(\mathfrak M)}$ on the grounds that it fails to be a cardinal in $\mathfrak M$. One always has that the cardinality of $\mathfrak c^{(HOD)}$ in $\mathfrak M$ is at most $\mathfrak c^{(\mathfrak M)}$ (as every real in HOD is a real in $\mathfrak M$). This is consistent with the observation that if a field has a degree-2 archimedean real-closed subfield in HOD, it also has one (namely, the same one) in $\mathfrak M$.
Dec 11, 2013 at 23:00	comment	added	Andreas Blass		@user38200 I'm not aware of any simpler description of that cardinal $\mathfrak c^{(HOD)}$. In particular, it could be larger than $\mathfrak c^{(\mathfrak M)}$ or smaller or equal to it.
Dec 11, 2013 at 21:00	comment	added	user38200		And what is the cardinality of continuum (in $\mathfrak{M}$) as percieved by HOD?
Dec 11, 2013 at 20:47	history	answered	Andreas Blass	CC BY-SA 3.0