Arcs in the Plane
classification
🧮 math.GN
math.LO
keywords
arcsplaneresultuncountablealephalthoughanalyticassuming
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Assuming PFA, every uncountable subset E of the plane meets some C^1 arc in an uncountable set. This is not provable from MA(aleph_1), although in the case that E is analytic, this is a ZFC result. The result is false in ZFC for C^2 arcs, and the counter-example is a perfect set.
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