Revised GCH or Would Cantor Have Understood

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Conference Proceeding

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The Continuum Hypothesis states that every infinite subset of the real line is bijective either with the set of natural numbers or with the set of real numbers. It was famously postulated by Cantor in 1878 and is known to be Independent of the usual axioms of set theory. Solution or acceptance of the non-solution to this and to the related Generalised Continuum Hypothesis have been a subject of constant interest in set theory. Which of these are philosophically acceptable? And which ones would meet the, it seems to us reasonable, requirement that Cantor should understand the answer to his own question? We’ll make a tour of some of the contemporary thoughts on this subject.


This presentation was part of the Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics in spring 2024.