Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 3
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Paulson, Lawrence C. 2015. A Mechanised Proof of Gödel’s Incompleteness Theorems Using Nominal Isabelle. Journal of Automated Reasoning, Vol. 55, Issue. 1, p. 1.

    Harrison, John Urban, Josef and Wiedijk, Freek 2014. Computational Logic.

    Manolios, Panagiotis and Vroon, Daron 2005. Ordinal Arithmetic: Algorithms and Mechanization. Journal of Automated Reasoning, Vol. 34, Issue. 4, p. 387.

  • LMS Journal of Computation and Mathematics, Volume 6
  • January 2003, pp. 198-248

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

  • Lawrence C. Paulson (a1)
  • DOI:
  • Published online: 01 February 2010

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.

Linked references
Hide All

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.

2B.A. Davey and H.A. Priestley , Introduction to lattices and order (Cambridge University Press, 1990).

4Kurt Gödel , ‘The consistency of the axiom of choice and of the generalized continuum hypothesis’, [3] 2627; first published in Proc. Nat. Acad. Sci.USA (1938) 556557.

11Tobias 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).

12Lawrence C. Paulson , ‘The foundation of a generic theorem prover‘, J. Automat. Reasoning 5 (1989) 363397.

13Lawrence C. Paulson , ‘Set theory for verification: I. From foundations to functions‘, J. Automat. Reasoning 11 (1993) 353389.

15Lawrence C. Paulson , ‘Set theory for verification: II. Induction and recursionJ. Automat. Reasoning 15 (1995) 167215.

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

18Lawrence C. Paulson , ‘The reflection theorem: a study in meta-theoretic reasoning’, [22] 377391.

19Lawrence C. Paulson and Krzysztof Grąbczewski , ‘Mechanizing set theory:cardinal arithmetic and the axiom of choice’, J. Automat. Reasoning 17 (1996) 291323.

21Martin Strecker , ‘Formal verification of a Java compiler in Isabelle’, [22] 6377.

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

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

LMS Journal of Computation and Mathematics
  • ISSN: -
  • EISSN: 1461-1570
  • URL: /core/journals/lms-journal-of-computation-and-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
Type Description Title
Supplementary Materials

JCM 6 Paulson Appendix A
Paulson Appendix A

 Unknown (749 KB)
749 KB