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Transfinite Update Procedures for Predicative Systems of Analysis

Author Federico Aschieri



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LIPIcs.CSL.2011.20.pdf
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Federico Aschieri

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Federico Aschieri. Transfinite Update Procedures for Predicative Systems of Analysis. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 20-34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)
https://doi.org/10.4230/LIPIcs.CSL.2011.20

Abstract

We present a simple-to-state, abstract computational problem, whose solution implies the 1-consistency of various systems of predicative Analysis and offers a way of extracting witnesses from classical proofs. In order to state the problem, we formulate the concept of transfinite update procedure, which extends Avigad's notion of update procedure to the transfinite and can be seen as an axiomatization of learning as it implicitly appears in various computational interpretations of predicative Analysis. We give iterative and bar recursive solutions to the problem.
Keywords
  • update procedure
  • epsilon substitution method
  • predicative classical analysis
  • bar recursion

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