dc.date.accessioned | 2024-03-19T16:05:42Z | |
dc.date.available | 2024-03-19T16:05:42Z | |
dc.date.created | 2023-11-13T09:09:07Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | Normann, Dag Sanders, Sam . The Biggest Five of Reverse Mathematics. Journal of Mathematical Logic. 2023 | |
dc.identifier.uri | http://hdl.handle.net/10852/109829 | |
dc.description.abstract | The aim of Reverse Mathematics (RM for short) is to find the minimal axioms needed to prove a given theorem of ordinary mathematics. These minimal axioms are almost always equivalent to the theorem, working over the base theory of RM, a weak system of computable mathematics. The Big Five phenomenon of RM is the observation that a large number of theorems from ordinary mathematics are either provable in the base theory or equivalent to one of only four systems; these five systems together are called the ‘Big Five’. The aim of this paper is to greatly extend the Big Five phenomenon as follows: there are two supposedly fundamentally different approaches to RM where the main difference is whether the language is restricted to second-order objects or if one allows third-order objects. In this paper, we unite these two strands of RM by establishing numerous equivalences involving the second-order Big Five systems on one hand, and well-known third-order theorems from analysis about (possibly) discontinuous functions on the other hand. We both study relatively tame notions, like cadlag or Baire 1, and potentially wild ones, like quasi-continuity. We also show that slight generalizations and variations of the aforementioned third-order theorems fall far outside of the Big Five. | |
dc.language | EN | |
dc.rights | Attribution 4.0 International | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.title | The Biggest Five of Reverse Mathematics | |
dc.title.alternative | ENEngelskEnglishThe Biggest Five of Reverse Mathematics | |
dc.type | Journal article | |
dc.creator.author | Normann, Dag | |
dc.creator.author | Sanders, Sam | |
cristin.unitcode | 185,15,13,0 | |
cristin.unitname | Matematisk institutt | |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 2 | |
dc.identifier.cristin | 2195488 | |
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=Journal of Mathematical Logic&rft.volume=&rft.spage=&rft.date=2023 | |
dc.identifier.jtitle | Journal of Mathematical Logic | |
dc.identifier.pagecount | 0 | |
dc.identifier.doi | https://doi.org/10.1142/S0219061324500077 | |
dc.type.document | Tidsskriftartikkel | |
dc.type.peerreviewed | Peer reviewed | |
dc.source.issn | 0219-0613 | |
dc.type.version | AcceptedVersion | |