FOM: Does Mathematics Need New Axioms?

[Harvey Friedman]

In 10:59AM  5/1/00, I wrote

>Boolean relation theory, and its expected extensions, seem to be developing
>all of these features. These expected extensions are expected to give
>Pi-0-1 statements about finite functions equivalent to the consistency of
>any large cardinal axioms yet considered, including the highest ones
>incompatible with the axiom of choice.

This is unclear. Replace "incompatible with the axiom of choice" by

"apparently compatible with ZF yet incompatible with ZFC, such as j:V into V."