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In Ben-David et al.'s "Learnability Can Be Undecidable," they prove anindependence result in theoretical machine learning. In particular, they definea new type of learnability, called Estimating The Maximum (EMX) learnability.They argue that this type of learnability fits in with other notions such asPAC learnability, Vapnik's statistical learning setting, and other generallearning settings. However, using some set-theoretic techniques, they show thatsome learning problems in the EMX setting are independent of ZFC. Specificallythey prove that ZFC cannot prove or disprove EMX learnability of the finitesubsets on the [0,1] interval. Moreover, the way they prove it shows that therecan be no characteristic dimension for EMX; and, hence, for general learningsettings. Here, I will explain their findings, discuss some limitations onthose findings, and offer some suggestions about how to excise thatundecidability. Parts 2-3 will explain the results of the paper, part 4-5 willdiscuss some limitations and next steps, and I will conclude in part 6.

Learnability Can Be Independent of ZFC Axioms: Explanations and Implications