Abstract
We introduce a class of First Order axiom systems which can simultaneously verify their own consistency and prove more Π1 theorems than Peano Arithmetic. Despite these strengths, our axiom systems do not violate Godel's Incompleteness Theorem because they treat multiplication as a partial function.
Partially funded by NSF 9060509.
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Dan Willard, E. (1993). Self-verifying axiom systems. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1993. Lecture Notes in Computer Science, vol 713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022580
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DOI: https://doi.org/10.1007/BFb0022580
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