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    Rosser's 1936 result shows weaker consistency suffices fo... — Carmelics
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    Challenges→For all natural numbers n, F proves the negation of Prf_F(n, ⌜G_F⌝)

    Rosser's 1936 result shows weaker consistency suffices for incompleteness, but the specific claim about provable negations for all n retains sensitivity to the consistency assumption's justificatory source.

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    Key Terms

    Justificatory source(as relating to why we trust assumptions)
    The underlying reason or foundation that explains why we should believe or accept something as true.
    Provable negations(as a technical concept in logic)
    Statements of the form 'not X' that a logical system can prove to be true using its own rules and axioms.
    Rosser(as a historical figure in logic)
    Barkley Rosser was a 20th-century mathematician and logician who proved important results about the limits of what formal systems can prove about themselves.
    consistency(Syntactic concept in many-sorted logic)
    The syntactic counterpart of satisfiability; corresponds to satisfiability in the same sense as ⊢ corresponds to ⊨
    incompleteness(Philosophy of mathematics / formal systems)

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    The property of a formal system whereby there exist true statements within the system that cannot be proven by the system itself.

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    For all natural numbers n, F proves the negation of Prf_F(n, ⌜G_F⌝)

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