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The Relative Consistency of the Axiom of Choice Mechanized Using Isabelle⁄zf

  • Lawrence C. Paulson (a1)
Abstract
Abstract

The proof of the relative consistency of the axiom of choice has been mechanized using Isabelle⁄ZF, building on a previous mechanization of the reflection theorem. The heavy reliance on metatheory in the original proof makes the formalization unusually long, and not entirely satisfactory: two parts of the proof do not fit together. It seems impossible to solve these problems without formalizing the metatheory. However, the present development follows a standard textbook, Kenneth Kunen's Set theory: an introduction to independence proofs, and could support the formalization of further material from that book. It also serves as an example of what to expect when deep mathematics is formalized.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

8 Florian Kammüller , Markus Wenzel and Lawrence C. Paulson ‘Locales: a sectioning concept for Isabelle’, Theorem proving in higher order logics: TPHOLs '99, Lecture Notes in Comput. Sci. 1690 (ed. Yves Bertot , Gilles Dowek , André Hirschowitz , Christine Paulin and Laurent Théry , Springer, 1999) 149165.

11 Tobias Nipkow , Lawrence C. Paulson and Markus Wenzel , Isabelle⁄HOL: a proof assistant for higher-order logic, Lecture Notes in Comput. Sci. Tutorial 2283 (Springer, 2002).

16 Lawrence C. Paulson , ‘Proving properties of security protocols by induction‘, 10th Computer Security Foundations Workshop (IEEE Computer Society Press, 1997) 7083.

22 Andrei Voronkov , ed. Automated deduction – CADE-18 International Conference, Lecture Notes in Artificial Intelligence 2392 (Springer, 2002).

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LMS Journal of Computation and Mathematics
  • ISSN: -
  • EISSN: 1461-1570
  • URL: /core/journals/lms-journal-of-computation-and-mathematics
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Supplementary Materials

JCM 6 Paulson Appendix A
Paulson Appendix A

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