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math.LO2024
Incompleteness theorems via Turing category
Yasha Savelyev
We give a reframing of Godel's first and second incompleteness theorems that applies even to some undefinable theories of arithmetic. The usual Hilbert-Bernays provability conditio…
math.LO2022
Incompleteness for stably computable formal systems
Yasha Savelyev
We prove, for stably computably enumerable formal systems, direct analogues of the first and second incompleteness theorems of Gödel. A typical stably computably enumerable set is…