Freiling axiom of symmetry
= Freiling axiom of symmetry
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{title2=$A_{<\omega_1}(\mathbb R)$}
= Freiling's axiom of symmetry
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{synonym}
Every function $f:\mathbb R\to[\mathbb R]^{<\omega_1}$ has reals $x,y$ with $x\notin f(y)$ and $y\notin f(x)$. The values are countable <subsets>. Requiring distinct witnesses is equivalent, by first adjoining $x$ to $f(x)$. The <Freiling theorem> identifies this axiom with the negation of the <Continuum hypothesis> in <ZFC>.