Subjective probabilities are inconsistent in any model which includes Peano arithmetic by straightforward application of Gödel's incompleteness theorems.

Did you mean to say incomplete (eg, implying that some small class of bizarrely constructed theorems about subjective probability can't be proven or disproven)?

Because the standard difficulties that Godel's theorem introduces to Peano arithmetic wouldn't render subjective probabilities inconsistent (eg, no theorems about subjective probability could be proven).