Towards Limit Computable Mathematics

@inproceedings{Hayashi2000TowardsLC,
  title={Towards Limit Computable Mathematics},
  author={Susumu Hayashi and Masahiro Nakata},
  booktitle={TYPES},
  year={2000}
}
The notion of Limit-Computable Mathematics (LCM) will be introduced. LCM is a fragment of classical mathematics in which the law of excluded middle is restricted to ?20-formulas. We can give an accountable computational interpretation to the proofs of LCM. The computational content of LCM-proofs is given by Gold's limiting recursive functions, which is the fundamentalno tion of learning theory. LCM is expected to be a right means for "Proof Animation", which was introduced by the first author… 
Mathematics Based on Learning
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A mathematics of which foundation itself is learning theoretic will be introduced, called Limit-Computable Mathematics, which was originally introduced as a means for "Proof Animation," which is expected to make interactive formal proof development easier.
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Restricted Limits on Natural Functions with Arithmetical Graphs
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    Rev. Colomb. de Computación
  • 2003
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The arithmetical class of thegraph of the function F is investigated, where the respective classes of the graph of f and the set A are known, and the corollary for the Turing degrees of F is formulated.
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