An elementary proof that the Borel class of the reals has cardinality continuum
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We give a recursion-like theorem which enables us to encode the elements of the real Borel class by infinite sequences of integers. This fact implies that the cardinality of the Borel class is not above continuum, without depending on cumbrous tools like transfinite induction and Suslin operation.
Key words and phrasesBorel set Solovay’s encoding intersection principle of hulls
Mathematics Subject Classification28A05 03E15
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The author thanks the anonymous referee for the valuable comments.
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