ON THE DECIDABILITY OF THE ${{\rm{\Sigma }}_2}$ THEORIES OF THE ARITHMETIC AND HYPERARITHMETIC DEGREES AS UPPERSEMILATTICES.
We establish the decidability of the ${{\rm{\Sigma }}_2}$ theory of both the arithmetic and hyperarithmetic degrees in the language of uppersemilattices, i.e., the language with ≤, 0 , and $\sqcup$. This is achieved by using Kumabe-Slaman forcing, along with other known results, to show given finite...
| Publicado en: | Journal of Symbolic Logic Vol. 82; no. 4; pp. 1496 - 1519 |
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| Formato: | Artículo |
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Cambridge University Press
Dec2017
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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=127197707&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 127197707 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00224812 3TY jtl: Journal of Symbolic Logic issn: 00224812 maglogo: N pubinfo: dt: Dec2017 vid: 82 iid: 4 pid: 15979 pub: Cambridge University Press artinfo: ui: 127197707 10.1017/jsl.2017.51 ppf: 1496 ppct: 23 formats: tig: atl: ON THE DECIDABILITY OF THE ${{\rm{\Sigma }}_2}$ THEORIES OF THE ARITHMETIC AND HYPERARITHMETIC DEGREES AS UPPERSEMILATTICES. aug: au: BARNES, JAMES S. affil: DEPARTMENT OF MATHEMATICS 310 MALOTT HALL CORNELL UNIVERSITY ITHACA, NY 14853, USA su: Recursion theory Algorithmic randomness Topological degree Applied mathematics Approximation theory Algebraic logic sug: subj: Recursion theory Algorithmic randomness Topological degree Applied mathematics Approximation theory Algebraic logic keyword: 03D30 arithmetic degrees degree theory hyperarithmetic degrees recursion theory ab: We establish the decidability of the ${{\rm{\Sigma }}_2}$ theory of both the arithmetic and hyperarithmetic degrees in the language of uppersemilattices, i.e., the language with ≤, 0 , and $\sqcup$. This is achieved by using Kumabe-Slaman forcing, along with other known results, to show given finite uppersemilattices ${\cal M}$ and ${\cal N}$, where ${\cal M}$ is a subuppersemilattice of ${\cal N}$, that every embedding of ${\cal M}$ into either degree structure extends to one of ${\cal N}$ iff ${\cal N}$ is an end-extension of ${\cal M}$. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2017 holdings: @attributes: islocal: N |
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