Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 5
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Carl, Merlin 2016. Infinite time recognizability from generic oracles and the recognizable jump operator1. Computability, p. 1.

    Ackerman, Nathanael L. Freer, Cameron E. and Lubarsky, Robert S. 2015. 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science. p. 523.

    Klev, Ansten Mørch 2009. Infinite time extensions of Kleene’s $${\mathcal{O}}$$. Archive for Mathematical Logic, Vol. 48, Issue. 7, p. 691.

    Welch, P.D. 2009. Characteristics of discrete transfinite time Turing machine models: Halting times, stabilization times, and Normal Form theorems. Theoretical Computer Science, Vol. 410, Issue. 4-5, p. 426.

    Welch, P.D. 2001. On Gupta-Belnap Revision Theories of Truth, Kripkean Fixed Points, and The Next Stable Set. Bulletin of Symbolic Logic, Vol. 7, Issue. 03, p. 345.


Eventually infinite time Turing machine degrees: infinite time decidable reals

  • P.D. Welch (a1) (a2)
  • DOI:
  • Published online: 01 March 2014

We characterise explicitly the decidable predicates on integers of Infinite Time Turing machines, in terms of admissibility theory and the constructible hierarchy. We do this by pinning down ζ, the least ordinal not the length of any eventual output of an Infinite Time Turing machine (halting or otherwise); using this the Infinite Time Turing Degrees are considered, and it is shown how the jump operator coincides with the production of mastercodes for the constructible hierarchy; further that the natural ordinals associated with the jump operator satisfy a Spector criterion, and correspond to the Lζ-stables. It also implies that the machines devised are “Σ2 Complete” amongst all such other possible machines. It is shown that least upper bounds of an “eventual jump” hierarchy exist on an initial segment.

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]K.J. Barwise , Admissible sets and structures, Perspectives in Mathematical Logic, Springer Verlag, Berlin, Heidelberg, 1975.

[3]K. Devlin , Constructibility, Perspectives in Mathematical Logic, Springer Verlag, Berlin, Heidelberg, 1984.

[6]A.S. Kechris , The theory of countable analytic sets, Transactions of the American Mathematical Society, vol. 202 (1975), pp. 259–297.

[7]P.D. Welch , The length of infinite time Turing degree computations, Bulletin of the London Mathematical Society, vol. 32 (2000), no. 2, pp. 129–136.

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? *