Abstract.
The infinite time Turing machine analogue of Post's problem, the question whether there are semi-decidable supertask degrees between 0 and the supertask jump 0∇, has in a sense both positive and negative solutions. Namely, in the context of the reals there are no degrees between 0 and 0∇, but in the context of sets of reals, there are; indeed, there are incomparable semi-decidable supertask degrees. Both arguments employ a kind of transfinite-injury construction which generalizes canonically to oracles.
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Received: 31 August 1998 / Published online: 12 July 2002
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Hamkins, J., Lewis, A. Post's problem for supertasks has both positive and negative solutions. Arch. Math. Logic 41, 507–523 (2002). https://doi.org/10.1007/s001530100112
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DOI: https://doi.org/10.1007/s001530100112