Skip to main content
×
Home
    • Aa
    • Aa

On the intuitionistic strength of monotone inductive definitions

  • Sergei Tupailo (a1)
Abstract
Abstract.

We prove here that the intuitionistic theory T0↾ + UMIDN. or even EETJ↾ + UMIDN, of Explicit Mathematics has the strength of –CA0. In Section 1 we give a double-negation translation for the classical second-order μ-calculus, which was shown in [Mö02] to have the strength of –CA0. In Section 2 we interpret the intuitionistic μ-calculus in the theory EETJ↾ + UMIDN. The question about the strength of monotone inductive definitions in T0 was asked by S. Feferman in 1982, and — assuming classical logic — was addressed by M. Rathjen.

Copyright
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.

[Fef82] S. Feferman , Monotone inductive definitions, The L. E. J. Brouwer centenary symposium ( A. S. Troelstra and D. van Dallen , editors), North-Holland, Amsterdam, 1982, pp. 7789.

[GRS97] T. Glaß , M. Rathjen , and A. Schlüter , On the proof-theoretic strength of monotone induction in explicit mathematics, Annals of Pure and Applied Logic, vol. 85 (1997), pp. 146.

[Tak89] S. Takahashi , Monotone inductive definitions in a constructive theory of functions and classes, Annals of Pure and Applied Logic, vol. 42 (1989), pp. 255297.

[Tu03] S. Tupailo , Realization of constructive set theory into Explicit Mathematics: a lower bound for impredicative Mahlo universe, Annals of Pure and Applied Logic, vol. 120 (2003), no. 1–3, pp. 165196.

Recommend this journal

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

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 1 *
Loading metrics...

Abstract views

Total abstract views: 37 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd June 2017. This data will be updated every 24 hours.