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Results tagged with large-cardinals
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user 61785
3
votes
Accepted
Consistency of the size of the least real-valued measurable cardinal, vis-a-vis the continuum
All of them are equiconsistent with the existence of a measurable cardinal. I find that a nice reference for this stuff, in addition to Solovay's article, is Jech's Set Theory: Third Millennium Editio …
- 3,768
3
votes
Reference: If $X$ is metrizable, then $X$ is realcompact iff $|X|$ is non-measurable
Here is some information on the history of the result, which was actually proven before Shirota's 1952 theorem. It was proved in 1948 by Marczewski and Sikorski as Theorem VI in:
Marczewski, E.; Sikor …
- 3,768