Journal of Symbolic Logic

Eventually Infinite Time Turing Machine Degrees: Infinite Time Decidable Reals

P. D. Welch

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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 $\zeta$, 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 L$_\zeta$-stables. It also implies that the machines devised are "$\Sigma_2$ Complete" amongst all such other possible machines. It is shown that least upper bounds of an "eventual jump" hierarchy exist on an initial segment.

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J. Symbolic Logic, Volume 65, Issue 3 (2000), 1193-1203.

First available in Project Euclid: 6 July 2007

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Welch, P. D. Eventually Infinite Time Turing Machine Degrees: Infinite Time Decidable Reals. J. Symbolic Logic 65 (2000), no. 3, 1193--1203.

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