Abstract
We discuss a proof of the wellfounded induction theorem for the ordinals up to ε 0. The proof is performed on the embedding of ACL2 in HOL-4, thus providing logical justification for that embedding and supporting the claim that the ACL2 logic has a model.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Franzen, T.: Inexhaustibility, a non-exhaustive treatment. Lecture Notes in Logic, vol. 16. A.K. Peters (2004)
Gentzen, G.: The consistency of elementary number theory. In: Szabo, M.E. (ed.) The Collected Papers of Gerhard Gentzen. Studies in Logic and the Foundations of Mathematics, North Holland, Amsterdam (1969)
Gentzen, G.: Provabillity and nonprovability of restricted transfinite induction in elementary number theory. In: Szabo, M.E. (ed.) The Collected Papers of Gerhard Gentzen. Studies in Logic and the Foundations of Mathematics, North Holland, Amsterdam (1969)
Goodstein, R.: On the restricted ordinal theorem. Journal of Symbolic Logic 9, 33–41 (1944)
Gordon, M.J.C., Hunt, W.A., Kaufmann, M., Reynolds, J.: An embedding of the ACL2 logic in HOL. In: Proceedings of ACL2 2006. ACM International Conference Proceeding Series, vol. 205, pp. 40–46. ACM Press, New York (2006)
Gordon, M.J.C., Hunt, W.A., Kaufmann, M., Reynolds, J.: An integration of HOL and ACL2. In: Proceedings of FMCAD 2006, pp. 153–160. IEEE Computer Society Press, Los Alamitos (2006)
Huffman, B.: Countable ordinals. Isabelle Archive of Formal Proofs (November 2005)
Kaufmann, M., Moore, J.S.: Structured theory development for a mechanized logic. Journal of Automated Reasoning 26(2), 161–203 (2001)
Manolios, P., Vroon, D.: Ordinal arithmetic: Algorithms and mechanization. Journal of Automated Reasoning, 1–37 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kaufmann, M., Slind, K. (2007). Proof Pearl: Wellfounded Induction on the Ordinals Up to ε 0 . In: Schneider, K., Brandt, J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2007. Lecture Notes in Computer Science, vol 4732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74591-4_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-74591-4_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74590-7
Online ISBN: 978-3-540-74591-4
eBook Packages: Computer ScienceComputer Science (R0)