Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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GOODSTEIN'S GENERALIZED THEOREM: FROM ROOTED TREE REPRESENTATIONS TO THE HYDRA GAME

  • LEONARDIS, A. (Department of Mathematics and Computer Science, University of Calabria) ;
  • D'ATRI, G. (Department of Mathematics and Computer Science, University of Calabria) ;
  • ZANARDO, E. (Department of Digital Innovation, University of Nicosia)
  • Received : 2021.06.29
  • Accepted : 2022.04.20
  • Published : 2022.09.30
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Abstract

A hereditary base-b representation, used in the celebrated Goodstein's theorem, can easily be converted into a labeled rooted tree. In this way it is possible to give a more elementary geometric proof of the aforementioned theorem and to establish a more general version, geometrically proved. This view is very useful for better understanding the underlying logical problems and the need to use transfinite induction in the proof. Similar problems will then be considered, such as the so-called "hydra game".

Keywords

Acknowledgement

This work has been partially supported by POR Calabria FESR-FSE 2014-2020, with the grant for research project "IoT&B", CUP J48C17000230006.

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