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arxiv: 0906.2753 · v1 · submitted 2009-06-15 · 🧮 math.GN · math.LO

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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