Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 2
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Jäger, Gerhard and Studer, Thomas 2011. A Buchholz Rule for Modal Fixed Point Logics. Logica Universalis, Vol. 5, Issue. 1, p. 1.


    Aehlig, Klaus 2008. Parameter-free polymorphic types. Annals of Pure and Applied Logic, Vol. 156, Issue. 1, p. 3.


    ×

Induction and inductive definitions in fragments of second order arithmetic

  • Klaus Aehlig (a1)
  • DOI: http://dx.doi.org/10.2178/jsl/1129642116
  • Published online: 01 March 2014
Abstract
Abstract

A fragment with the same provably recursive functions as n iterated inductive definitions is obtained by restricting second order arithmetic in the following way. The underlying language allows only up to n + 1 nested second order quantifications and those are in such a way. that no second order variable occurs free in the scope of another second order quantifier. The amount of induction on arithmetical formulae only affects the arithmetical consequences of these theories, whereas adding induction for arbitrary formulae increases the strength by one inductive definition.

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.

[1]P. Aczel , An introduction to inductive definitions, Handbook of Mathematical Logic (J. Barwise , editor), Studies in Logic and the Foundations of Mathematics, vol. 90, chapter C.7, North-Holland Publishing Company, 1977, pp. 739782.

[3]K. Aehlig and J. Johannsen , An elementary fragment of second-order lambda-calculus, ACM Transactions on Computational Logic, vol. 6 (2005), no. 2, pp. 468480.

[4]T. Altenkirch and T. Coquand , A finitary subsystem of the polymorphic lambda-calculus, Proceedings of the 5th international conference on typed lambda caculi and applications (TLCA '01) (S. Abramsky , editor), Lecture Notes in Computer Science, vol. 2044, Springer Verlag, Berlin, 2001, pp. 2228.

[5]T. Arai , A slow growing analogue to Buchholz' proof, Annals of Pure and Applied Logic, vol. 54 (1991), pp. 101120.

[9]S. Feferman , Formal theories for transfinite iterations of generalized inductive definitions, Intuitionism and proof theory (proceedings of the summer conference at Buffalo N. Y. 1968) (A. Kino , J. Myhill , and R. E. Vesley , editors), Studies in Logic and the Foundation of Mathematics, North-Holland Publishing Company, Amsterdam, 1970, pp. 303326.

[12]D. Leivant , Finitely stratified polymorphism, Information and Computation, vol. 93 (1991), pp. 93113.

[15]G. Takeuti , Consistency proofs of subsystems of classical analysis, Annals of Mathematics, vol. 86 (1967), pp. 299348.

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? *
×