Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Throwing Darts at a Ruler: Unpacking the Intuition Behind Freiling's
  Axiom of Symmetry   It is well-known that the Continuum Hypothesis (CH) is independent of the
other axioms of Zermelo-Fraenkel set theory with choice (ZFC). This raises the
question of whether an intuitive justification exists for CH as an additional
axiom, or conversely whether it is more intuitive to deny CH. Freiling's Axiom
of Symmetry (AS) is one candidate for an intuitively justifiable axiom that,
when appended to ZFC, is equivalent to the denial of CH. The intuition relies
on a probabalistic argument, usually cast in terms of throwing random darts at
the real line, and has been defended by researchers as well as popular writers.
In this note, the intuitive argument is reviewed. Following William Abram, it
is suggested that while accepting CH leads directly to a counterexample to AS,
this is not necessarily fatal to our intuition. Instead, we suggest, it serves
to alert us to the error in a naive intuition that leaps too readily from the
near-certainty of individual events to near-certainty of a joint event.

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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph