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Machine learning and the continuum hypothesis. (English) Zbl 1446.03085

Summary: In January 2019 the journal Nature reported on an exciting development in Machine Learning: the very first issue of the journal Nature Machine Intelligence contains a paper that describes a learning problem whose solvability is neither provable nor refutable on the basis of the standard ZFC axioms of Set Theory. In this note K. P. Hart describes what the fuss is all about and indicates that maybe the problem is not so undecidabie after all.

MSC:

03E50 Continuum hypothesis and Martin’s axiom
03E10 Ordinal and cardinal numbers
03D35 Undecidability and degrees of sets of sentences
68V15 Theorem proving (automated and interactive theorem provers, deduction, resolution, etc.)
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Full Text: arXiv