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Mar 17, 2014 at 1:37 comment added Noah Schweber (Although I'll admit to an ulterior motive: any opportunity to mention Miller's bizarre Borel sets is a good one, to my mind.)
Mar 17, 2014 at 1:35 comment added Noah Schweber That's a good point - although that definition is (?) $\Delta^1_2$, whereas if something like Miller's Borel strictly Dedekind finite set lacked FPP, then we'd have a definition of much lower complexity, and probably(?) close to minimal possible complexity - at least, among topological spaces whose underlying set is a set of reals.
Mar 17, 2014 at 1:29 comment added Joel David Hamkins One could consider "the unit interval of $L$" as a definition, and my example would still be an example of the kind you seek, provided that $\mathbb{R}^V\subset L$.
Mar 16, 2014 at 22:52 history edited Noah Schweber CC BY-SA 3.0
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Mar 16, 2014 at 22:32 history answered Noah Schweber CC BY-SA 3.0