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KnaveOfAllTrades comments on Consistent extrapolated beliefs about math? - Less Wrong Discussion
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(A): There exists a function f:R->R
and the axioms, for all r in R:
(A_r): f(r)=0
(The graph of f is just the x-axis.)
This might be expressible with a finite axiomatisation (e.g. by building functions and arithmetic in ZFC), and indeed I've given a finite schema, but I'm not sure it's 'fair' to ask for an example of a theory that cannot be compressed beyond uncountably many axioms; that would be a hypertask, right? I think that's what Joshua's getting at in the sibling to this comment.