Who believes/believed that set theory is/was inconsistent?

25 years ago (it might have been) I think I heard John Mayberry say that
someone believed that set theory was inconsistent and was trying to
prove it. Indeed, he said that the same person doubted the consistency
of PA. He named the person, but I cannot remember the name.

To whom was Mayberry referring?

The set theory may have been ZF but I don't recall precisely.

--
I don't know who you are Sir, or where you come from,
but you've done me a power of good.
.

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