A definable number is a real number \(a\) such that, given a formula in the language of set theory \(\varphi\), \(\varphi(a)\) is true. Thus, definable numbers include constants like \(0, 1, e, \pi\) and so on.

What is the Lebesgue measure of the set of all definable numbers in the interval \((0,1)\)?

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