dc.date.accessioned | 2022-01-25T18:39:56Z | |
dc.date.available | 2022-12-16T23:45:58Z | |
dc.date.created | 2021-12-28T13:45:55Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Normann, Dag Sanders, Sam . Betwixt Turing and Kleene. Lecture Notes in Computer Science (LNCS). 2021, 13137, 236-252 | |
dc.identifier.uri | http://hdl.handle.net/10852/90074 | |
dc.description.abstract | Turing’s famous ‘machine’ model constitutes the first intuitively convincing framework for computing with real numbers. Kleene’s computation schemes S1–S9 extend Turing’s approach and provide a framework for computing with objects of any finite type. Various research programs have been proposed in which higher-order objects, like functions on the real numbers, are represented/coded as real numbers, so as to make them amenable to the Turing framework. It is then a natural question whether there is any significant difference between the Kleene approach or the Turing-approach-via-codes. Continuous functions being well-studied in this context, we study functions of bounded variation, which have at most countably many points of discontinuity. A central result is the Jordan decomposition theorem that a function of bounded variation on [0, 1] equals the difference of two monotone functions. We show that for this theorem and related results, the difference between the Kleene approach and the Turing-approach-via-codes is huge, in that full second-order arithmetic readily comes to the fore in Kleene’s approach, in the guise of Kleene’s quantifier ∃3. | |
dc.language | EN | |
dc.title | Betwixt Turing and Kleene | |
dc.type | Journal article | |
dc.creator.author | Normann, Dag | |
dc.creator.author | Sanders, Sam | |
cristin.unitcode | 185,15,13,65 | |
cristin.unitname | Flere komplekse variable, logikk og operatoralgebraer | |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 1 | |
dc.identifier.cristin | 1972460 | |
dc.identifier.bibliographiccitation | info:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Lecture Notes in Computer Science (LNCS)&rft.volume=13137&rft.spage=236&rft.date=2021 | |
dc.identifier.jtitle | Lecture Notes in Computer Science (LNCS) | |
dc.identifier.volume | 13137 | |
dc.identifier.startpage | 236 | |
dc.identifier.endpage | 252 | |
dc.identifier.doi | https://doi.org/10.1007/978-3-030-93100-1_15 | |
dc.identifier.urn | URN:NBN:no-92728 | |
dc.type.document | Tidsskriftartikkel | |
dc.type.peerreviewed | Peer reviewed | |
dc.source.issn | 0302-9743 | |
dc.identifier.fulltext | Fulltext https://www.duo.uio.no/bitstream/handle/10852/90074/1/525557_1_En_15_Chapter_OnlinePDF.pdf | |
dc.type.version | AcceptedVersion | |