Church, Cardinal and Ordinal Representations of Integers and Kolmogorov complexity

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dc.creatorFerbus-Zanda, Marie
dc.creatorGrigorieff, Serge
dc.date2008-01-02
dc.date.accessioned2026-07-07T08:52:07Z
dc.date.available2026-07-07T08:52:07Z
dc.descriptionWe consider classical representations of integers: Church's function iterators, cardinal equivalence classes of sets, ordinal equivalence classes of totally ordered sets. Since programs do not work on abstract entities and require formal representations of objects, we effectivize these abstract notions in order to allow them to be computed by programs. To any such effectivized representation is then associated a notion of Kolmogorov complexity. We prove that these Kolmogorov complexities form a strict hierarchy which coincides with that obtained by relativization to jump oracles and/or allowance of infinite computations.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/0801.0349
dc.identifierhttp://arxiv.org/abs/0801.0349
dc.identifierDans Denis Richard's 60th Biirthday Conference - Denis Richard's 60th Biirthday Conference, France (2002)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145173
dc.subjectLogic
dc.subjectComputational Complexity
dc.subjectLogic in Computer Science
dc.titleChurch, Cardinal and Ordinal Representations of Integers and Kolmogorov complexity
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