Acta Mathematica Hungarica

, Volume 159, Issue 1, pp 124–130 | Cite as

An elementary proof that the Borel class of the reals has cardinality continuum

  • Z. KánnaiEmail author


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 phrases

Borel set Solovay’s encoding intersection principle of hulls 

Mathematics Subject Classification

28A05 03E15 


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The author thanks the anonymous referee for the valuable comments.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of MathematicsCorvinus UniversityBudapestHungary

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