Ok discussion; the suggestion that the results given back by OracleT and OracleF are "equally valid" annoys me: mathematical logicians have the concept of Sigma^0_1-soundness here, which is something that, since the sentence "Oracle says 0=1 is true" is Sigma^0_1, the two higher level oracles disagree on and that there is a fact as to the matter as to whether such statements are true or not.