An Enhanced Theory of Infinite Time Register Machines
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Infinite time register machines
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A generalised dynamical system, infinite time register machines, and Π11-CA;0
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Ordinal computability uses ordinals instead of natural numbers in abstract machines like register or Turing machines. We give an overview of the computational strengths of *** -β -machines, where *** and β bound the time axis and the space axis of some machine model. The spectrum ranges from classical Turing computability to ***-***-computability which corresponds to Gödel 's model of constructible sets. To illustrate some typical techniques we prove a new result on Infinite Time Register Machines (= ***-*** -register machines) which were introduced in [6]: a real number x *** *** 2 is computable by an Infinite Time Register Machine iff it is Turing computable from some finitely iterated hyperjump 0(n ).