Here is the basic problem. I think that you can construct an appropriate liar’s sentence by using a Lipschitz function without an approximate fixed point. But someone might want to check that more carefully and write it up, to make sure and to see where the possible loopholes are. I think that it may not have ruled out this particular principle, just something slightly stronger (but the two were equivalent for the kinds of proof techniqeus we were considering).
Here is the basic problem. I think that you can construct an appropriate liar’s sentence by using a Lipschitz function without an approximate fixed point. But someone might want to check that more carefully and write it up, to make sure and to see where the possible loopholes are. I think that it may not have ruled out this particular principle, just something slightly stronger (but the two were equivalent for the kinds of proof techniqeus we were considering).