Answer by Noah Schweber for Why Godel have chosen $\omega$-consistency of a...
You're forgetting the historical context of the theorem.Prior to Godel's work, there is no reason to expect "$T\not\vdash\neg Con(T)$" to even make sense. By contrast, $\omega$-consistency makes...
View ArticleWhy Godel have chosen $\omega$-consistency of a theory instead of it proving...
Godel assumed $\omega$-consistency for his proof of the first incompleteness theorem to run. But, isn't it the case that if we assume that a theory $T$ is effective, complete and $\omega$-consistent,...
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