Switch to: References

Add citations

You must login to add citations.
  1. Supertasks.Jon Pérez Laraudogoitia - 2008 - Stanford Encyclopedia of Philosophy.
  • Taming Koepke's Zoo II: Register Machines.Merlin Carl - 2022 - Annals of Pure and Applied Logic 173 (3):103041.
  • Infinite Computations with Random Oracles.Merlin Carl & Philipp Schlicht - 2017 - Notre Dame Journal of Formal Logic 58 (2):249-270.
    We consider the following problem for various infinite-time machines. If a real is computable relative to a large set of oracles such as a set of full measure or just of positive measure, a comeager set, or a nonmeager Borel set, is it already computable? We show that the answer is independent of ZFC for ordinal Turing machines with and without ordinal parameters and give a positive answer for most other machines. For instance, we consider infinite-time Turing machines, unresetting and (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Randomness Via Infinite Computation and Effective Descriptive Set Theory.Merlin Carl & Philipp Schlicht - 2018 - Journal of Symbolic Logic 83 (2):766-789.
    We study randomness beyond${\rm{\Pi }}_1^1$-randomness and its Martin-Löf type variant, which was introduced in [16] and further studied in [3]. Here we focus on a class strictly between${\rm{\Pi }}_1^1$and${\rm{\Sigma }}_2^1$that is given by the infinite time Turing machines introduced by Hamkins and Kidder. The main results show that the randomness notions associated with this class have several desirable properties, which resemble those of classical random notions such as Martin-Löf randomness and randomness notions defined via effective descriptive set theory such as${\rm{\Pi (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  • The Distribution of ITRM-Recognizable Reals.Merlin Carl - 2014 - Annals of Pure and Applied Logic 165 (9):1403-1417.
    Infinite Time Register Machines are a well-established machine model for infinitary computations. Their computational strength relative to oracles is understood, see e.g. , and . We consider the notion of recognizability, which was first formulated for Infinite Time Turing Machines in [6] and applied to ITRM 's in [3]. A real x is ITRM -recognizable iff there is an ITRM -program P such that PyPy stops with output 1 iff y=xy=x, and otherwise stops with output 0. In [3], it is (...))
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Optimal Results on Recognizability for Infinite Time Register Machines.Merlin Carl - 2015 - Journal of Symbolic Logic 80 (4):1116-1130.
  • Recognizable Sets and Woodin Cardinals: Computation Beyond the Constructible Universe.Merlin Carl, Philipp Schlicht & Philip Welch - 2018 - Annals of Pure and Applied Logic 169 (4):312-332.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations