[acchow]

  1 -> 0 = 0

What does this mean? Is the 0 after the equals the antecedent? Consequent?

[pmcjones]

(1 -> 0) = 0.

In other words, (true implies false) is false.

[acchow]

"is false" doesn't mean anything in Godel's system. That's too high level and imprecise. We're dealing with only symbol manipulation here. We only have provability (which really is "there exists a derivation for") - we don't have "truth".