Abstract
The main purpose of this paper is to answer a question raised by Grigorieff in [4]. In [4], Grigorieff proved that every infinite recursive linear ordering L is isomorphic to realtime linear ordering L′ whose universe is the binary representation of the natural numbers. Grigorieff’s proof involved two steps. First he showed that if a recursive linear ordering Lhas the property that Lhas a recursive sequence S = s 0 <L s < L … such that either S cofinal in L or S has a supremum in L or L has recursive sequence U = u 0 > L u 1 > L … such that U is coinitial in L or U has an infimum in L, then Lis recursively isomorphic to a realtime linear ordering L′ whose universe is the binary representation of the natural numbers.
Partially supported by NSF grant DMS-87-02473.
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© 1990 Birkhäuser Boston
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Remmel, J.B. (1990). When is every recursive linear ordering of type μ recursively isomorphic to a polynomial time linear ordering over the natural numbers in binary form?. In: Buss, S.R., Scott, P.J. (eds) Feasible Mathematics. Progress in Computer Science and Applied Logic, vol 9. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3466-1_18
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DOI: https://doi.org/10.1007/978-1-4612-3466-1_18
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