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New formally undecidable propositions: non-trivial lower bounds on proof complexity and related theorems

1991
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Theoretical Computer Science
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Luckhardt, H., New formally undecidable propositions: non-trivial lower bounds on proof complexity and related theorems, Theoretical Computer Science 83 (1991) 169-188. Within a formal theory T where a I-rule is provably valid and Gdel's second incompleteness theorem holds, it is not possible to prove any non-trivial lower bound LB, on proof complexity. Most calculi currently used in formalizing proofs are of this type. We give many sets of formulas where non-trivial lower bounds LB, are

doi:10.1016/0304-3975(91)90272-4
fatcat:sxrrh4cxefhknccipacsn4r3nu