Self-verifying axiom systems, the incompleteness theorem and related reflection principles

@article{Willard2001SelfverifyingAS,
  title={Self-verifying axiom systems, the incompleteness theorem and related reflection principles},
  author={Dan E. Willard},
  journal={Journal of Symbolic Logic},
  year={2001},
  volume={66},
  pages={536 - 596}
}
  • D. Willard
  • Published 1 June 2001
  • Mathematics
  • Journal of Symbolic Logic
Abstract We will study several weak axiom systems that use the Subtraction and Division primitives (rather than Addition and Multiplication) to formally encode the theorems of Arithmetic. Provided such axiom systems do not recognize Multiplication as a total function, we will show that it is feasible for them to verify their Semantic Tableaux, Herbrand, and Cut-Free consistencies. If our axiom systems additionally do not recognize Addition as a total function, they will be capable of… 
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