How am I supposed to read the P=?NP relativization proof? I am reading
Theodore Baker, John Gill, and Robert Solovay. Relativization of the P=?NP problem. Siam Journal of Computing, 4:432-442, 1975 
in particular the proof that there exist an oracle B such that P^B = NP^B on page 436. I have some questions and your help will be appreciated.
The procedure does not seem to be an oracle but a deterministic algorithm ... ?
Is this construction a counterexample to P = NP?
What does this mean "Run query machine P_i with oracle B_i on input x_i = 0^n?" Does it mean that P_i asks
a) if B_i accepts 0^n
b) if B_i accepts any string of lenght n
c) ONE BY ONE if B_i accepts a string of length n from the canonical enumeration?
- I assume that the set B or B_i is initially empty. Does it mean that the FIRST string of length n form the canonical enumeration will always be added?