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A Minimal Computational Theory of a Minimal Computational Universe

  • Arnon Avron
  • Liron CohenEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10703)

Abstract

In [3] a general logical framework for formalizing set theories of different strength was suggested. We here employ that framework, focusing on the exploration of computational theories. That is, theories whose set of closed terms suffices for denoting every concrete set (including infinite ones) that might be needed in applications, as well as for computations with sets. We demonstrate that already the minimal computational level of the framework, in which only a minimal computational theory and a minimal computational universe are employed, suffices for developing large portions of scientifically applicable mathematics.

Keywords

Formalized mathematics Computational theories Computational universes Rudimentary set theory 

Notes

Acknowledgements

The second author is supported by: Fulbright Post-doctoral Scholar program; Weizmann Institute of Science – National Postdoctoral Award program for Advancing Women in Science; Eric and Wendy Schmidt Postdoctoral Award program for Women in Mathematical and Computing Sciences.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Tel Aviv UniversityTel-AvivIsrael
  2. 2.Cornell UniversityIthacaUSA

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