Incompleteness is not a theorem of PA, unless PA is inconsistent. — TonesInDeepFreeze
The use of logical entailment predates model theory by decades — Tarskian
T ⊨S as a synonym for "S is true in T". — Tarskian
the Gödelian statements that cannot be expressed by language. There are uncountably many of those. — Tarskian
Gödel's incompleteness theorem proves that PA is inconsistent or incomplete. — Tarskian
That is a perfectly legitimate theorem in PA. — Tarskian
It does not prove that PA is incomplete. — Tarskian
That is a theorem in PA + Cons(PA). — Tarskian
hat is a perfectly legitimate theorem in PA. — Tarskian
I'm not sure about that; I'd have to think about it. — TonesInDeepFreeze
I don't think it's a theorem in PA, it's a theorem about PA. — fdrake
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