Sorry, we’re miscommunicating somewhere. What I’m saying is that e.g. given a set A of statements, I want the axiom asserting the existence of the set
%20%3E%201/2\}), i.e. the comprehension axiom applied to the condition
%20%3E%201/2). I don’t understand how this would lead to
%20=%20\mathbb{P}(x%20\notin%20x)); could you explain? (It seems like you’re talking about unrestricted comprehension of some sort; I’m just talking about allowing the condition in ordinary restricted comprehension to range over formulas in L’. Maybe the problem you have in mind only occurs in the unrestricted comprehension work which isn’t in this draft?)
Consider my proposed condition that ”T is consistent with A_mathbb{P} for any coherent distribution mathbb{P}”. To see that this is true for ZFC in the language L’, choose a standard model of ZFC in L and, for any function mathbb{P} from the sentences of L’ to
, extend it to a model in L’ by interpreting
) as
); unless I’m being stupid somehow, it’s clear that the extended model will satisfy ZFC-in-L’ + A_mathbb{P}.
It seems to me that the only parts of the proof that need to be re-thought are the arguments that (a) mathcal{A} and (b)
) are non-empty. Perhaps the easiest way to say the argument is that we extend (a) T or (b) TA_mathbb{P′} to some arbitrary complete theory
I understand what you are saying. You are completely right, thanks for the observation. I don’t have time to muck with the paper now, but it looks like this would work.
Sorry, we’re miscommunicating somewhere. What I’m saying is that e.g. given a set A of statements, I want the axiom asserting the existence of the set
Consider my proposed condition that ”T is consistent with A_mathbb{P} for any coherent distribution mathbb{P}”. To see that this is true for ZFC in the language L’, choose a standard model of ZFC in L and, for any function mathbb{P} from the sentences of L’ to
It seems to me that the only parts of the proof that need to be re-thought are the arguments that (a) mathcal{A} and (b)
I understand what you are saying. You are completely right, thanks for the observation. I don’t have time to muck with the paper now, but it looks like this would work.