[FOM] T + ~Con(T) Refutes Its Goedel Sentence

[Peter Smith]

Richard Heck writes

> The general observation, which is presumably well-known, but which I've 
> never seen mentioned in the textbooks from which I've taught, is that, 
> for sufficiently strong T, T + ~Con(T) proves the negation of that 
> theory's Goedel sentence.

For what it is worth, this explained and explored in my Introduction to 
Gödel's Theorems (§§34.1, 34.2 in the second edition).

-- 
Dr Peter Smith
http://logicmatters.net