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Discrete transfinite computation models

In S. B. Cooper & Andrea Sorbi (eds.), Computability in Context: Computation and Logic in the Real World. World Scientific. pp. 375--414 (2011)

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  1. A Note on the Physical Possibility of Transfinite Computation.Wayne Aitken & Jeffrey A. Barrett - 2010 - British Journal for the Philosophy of Science 61 (4):867-874.
    In this note, we consider constraints on the physical possibility of transfinite Turing machines that arise from how one models the continuous structure of space and time in one's best physical theories. We conclude by suggesting a version of Church's thesis appropriate as an upper bound for physical computation given how space and time are modeled on our current physical theories.
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  • Vom Zahlen Zu den Zahlen: On the Relation Between Computation and Arithmetical Structuralism.L. Horsten - 2012 - Philosophia Mathematica 20 (3):275-288.
    This paper sketches an answer to the question how we, in our arithmetical practice, succeed in singling out the natural-number structure as our intended interpretation. It is argued that we bring this about by a combination of what we assert about the natural-number structure on the one hand, and our computational capacities on the other hand.
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  • The Computational Strengths of Α-Tape Infinite Time Turing Machines.Benjamin Rin - 2014 - Annals of Pure and Applied Logic 165 (9):1501-1511.
    In [7], open questions are raised regarding the computational strengths of so-called ∞-α -Turing machines, a family of models of computation resembling the infinite-time Turing machine model of [2], except with α -length tape . Let TαTα denote the machine model of tape length α . Define that TαTα is computationally stronger than TβTβ precisely when TαTα can compute all TβTβ-computable functions ƒ: min2→min2 plus more. The following results are found: Tω1≻TωTω1≻Tω. There are countable ordinals α such that Tα≻TωTα≻Tω, the (...)
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