A generalised dynamical system, infinite time register machines, and Π11-CA;0

Authors:
Peter Koepke;Philip D. Welch
Affiliations:
Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany;School of Mathematics, University of Bristol, Clifton, Bristol, United Kingdom
Venue:
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
Year:
2011

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Abstract

We identify a number of theories of strength that of Π11- CA0. In particular: (a) the theory that the set of points attracted to the origin in a generalised transfinite dynamical system of any n-dimensional integer torus exists; (b) the theory asserting that for any Z ⊆ ω and n, the halting set HnZ of infinite time n-register machine with oracle Z exists.