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Tagged with formal-languages metamathematics
3 questions
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Is there an equivalent of the incompleteness theorems/halting problem in category theory?
Taking the doctrine of computational trinitarianism ( https://ncatlab.org/nlab/show/computational+trinitarianism ), if one understands the incompleteness theorems as the "logic" version, and ...
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Is there a formal notion of what we do when we 'Let X be ...'?
This is likely an elementary question to logicians or theoretical computer scientists, but I'm less than adequately informed on either topic and don't know where to find the answer. Please excuse the ...
8
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What assumptions and methodology do metaproofs of logic theorems use and employ?
In logic modules, theorems like Soundness and completeness of first order logic are proved. Later, Godel's incompleteness theorem is proved. May I ask what are assumed at the metalevel to prove such ...