Abstract
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.
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The author thanks the anonymous referee for the valuable comments.
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Kánnai, Z. An elementary proof that the Borel class of the reals has cardinality continuum. Acta Math. Hungar. 159, 124–130 (2019). https://doi.org/10.1007/s10474-019-00986-7
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DOI: https://doi.org/10.1007/s10474-019-00986-7