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Formalization of the Fundamental Group in Untyped Set Theory Using Auto2

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Abstract

We present a new framework for formalizing mathematics in untyped set theory using auto2. We demonstrate that many difficulties with using set theory for formalization of mathematics can be addressed by improvements to automation, without sacrificing the inherent flexibility of the logic. As applications, we formalize in Isabelle/FOL the entire chain of development from the axioms of set theory to the definition of the fundamental group of an arbitrary topological space. The auto2 prover is used as the sole automation tool, and enables succinct proof scripts throughout the project.

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Notes

  1. Code available at https://github.com/bzhan/auto2

  2. http://www.cs.nyu.edu/pipermail/fom/2014-October/018243.html

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Acknowledgements

The author would like to thank the anonymous reviewers for their helpful comments. Most of this work is completed while the author is at the Department of Mathematics at MIT, and supported by NSF Award No. 1400713. Part of the work is done at the Technical University of Munich, while the author is supported by DFG Grant NI 491/16-1.

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  1. Chair for Logic and Verification, Technical University of Munich, Munich, Germany

    Bohua Zhan

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  1. Bohua Zhan
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Correspondence to Bohua Zhan.

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Zhan, B. Formalization of the Fundamental Group in Untyped Set Theory Using Auto2. J Autom Reasoning 63, 517–538 (2019). https://doi.org/10.1007/s10817-018-9478-0

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  • DOI: https://doi.org/10.1007/s10817-018-9478-0

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