Learnability Can Be Independent of ZFC Axioms: Explanations and Implications — HN submission

Wed, 22 Jul 2026 15:02:26 GMT

Learnability Can Be Independent of ZFC Axioms (2019)

2 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Learnability Can Be Independent of ZFC Axioms: Explanations and Implications — mentioned by jsrozner

Sun, 19 Jul 2026 19:00:16 GMT

Has anyone here actually looked at the Shai Ben David (SBD) result? I did a final grad project on it recently for a class on incompleteness. In my view it's not really that interesting. For learnability to be undecidable, the cardinality of the continuum (size of the reals) must exceed \aleph_k for all finite k. ZFC does not bear upon this (CH is independent of ZFC), so this is a possible setting of the world, and therefore learnability can be undecidable. But say the size of the continuum is, e.g., \aleph_3, (in this case CH is false, but it's not "horribly false"), then SBD shows how to…

Paper and discussion history. A mention is not an endorsement.

Learnability Can Be Independent of ZFC Axioms: Explanations and Implications · HackerPapers discussions

Learnability Can Be Independent of ZFC Axioms: Explanations and Implications — HN submission

Learnability Can Be Independent of ZFC Axioms: Explanations and Implications — mentioned by jsrozner