WEAKLY 2-RANDOMS AND 1-GENERICS IN SCOTT SETS.
Let ${\cal S}$ be a Scott set, or even an <italic>ω</italic>-model of WWKL. Then for each <italic>A</italic> ε <italic>S</italic>, either there is <italic>X</italic> ε <italic>S</italic> that is weakly 2-random relative to <italic>A</italic>, or there is <italic>X</italic> ε <italic>S</italic> that...
| Publicado en: | Journal of Symbolic Logic Vol. 83; no. 1; pp. 392 - 395 |
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| Formato: | Artículo |
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Cambridge University Press
Mar2018
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=129383508&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 129383508 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00224812 3TY jtl: Journal of Symbolic Logic issn: 00224812 maglogo: N pubinfo: dt: Mar2018 vid: 83 iid: 1 pid: 15979 pub: Cambridge University Press artinfo: ui: 129383508 10.1017/jsl.2017.73 ppf: 392 ppct: 3 formats: tig: atl: WEAKLY 2-RANDOMS AND 1-GENERICS IN SCOTT SETS. aug: au: WESTRICK, LINDA BROWN affil: DEPARTMENT OF MATHEMATICS UNIVERSITY OF CONNECTICUT STORRS, CT, USA su: Topological degree Set theory Algorithmic randomness Semilattices Logic sug: subj: Topological degree Set theory Algorithmic randomness Semilattices Logic keyword: 03D28 03D32 03F35 algorithmic randomness degree theory genericity lattice embedding Scott set ab: Let ${\cal S}$ be a Scott set, or even an <italic>ω</italic>-model of WWKL. Then for each <italic>A</italic> ε <italic>S</italic>, either there is <italic>X</italic> ε <italic>S</italic> that is weakly 2-random relative to <italic>A</italic>, or there is <italic>X</italic> ε <italic>S</italic> that is 1-generic relative to <italic>A</italic>. It follows that if <italic>A</italic>,…,<italic>A</italic> ε <italic>S</italic> are noncomputable, there is <italic>X</italic> ε <italic>S</italic> such that each <italic>A</italic> is Turing incomparable with <italic>X</italic>, answering a question of Kučera and Slaman. More generally, any ∀∃ sentence in the language of partial orders that holds in ${\cal D}$ also holds in ${{\cal D}^{\cal S}}$ , where ${{\cal D}^{\cal S}}$ is the partial order of Turing degrees of elements of ${\cal S}$. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2018 holdings: @attributes: islocal: N |
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