On 2/9/2024 1:05 PM, Ross Finlayson wrote:

On 11/17/2016 01:32 AM, [email protected] wrote:

Does that mean that
the Godel´s reasoning isn't expressible in PM, or
that the ω-inconsistency imply inconsistency?

It's an interesting sort of question.

Also interesting:
Rosser's Trick (1936) upgrades
Godel´s provability predicate (1931) so that
essentially the same proof from
the same assumptions proves
incompleteness or _inconsistency_

https://en.wikipedia.org/wiki/Rosser%27s_trick
| While Gödel's original proof uses
| a sentence that says (informally)
| "This sentence is not provable",
| Rosser's trick uses
| a formula that says
| "If this sentence is provable,
| there is a shorter proof of its negation".

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