DEFINABILITY OF DERIVATIONS IN THE REDUCTS OF DIFFERENTIALLY CLOSED FIELDS.
Let ${\cal F}$ =(F; +, .,0, 1, D) be a differentially closed field. We consider the question of definability of the derivation D in reducts of ${\cal F}$ of the form ${\cal F}$R = (F; +, .,0, 1, P)P ε R where R is some collection of definable sets in ${\cal F}$. We give examples and nonexamples and...
| Published in: | Journal of Symbolic Logic Vol. 82; no. 4; pp. 1252 - 1278 |
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| Format: | Article |
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Cambridge University Press
Dec2017
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| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=127197708&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 127197708 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: 127197708 10.1017/jsl.2017.54 ppf: 1252 ppct: 26 formats: tig: atl: DEFINABILITY OF DERIVATIONS IN THE REDUCTS OF DIFFERENTIALLY CLOSED FIELDS. aug: au: ASLANYAN, VAHAGN affil: MATHEMATICAL INSTITUTE UNIVERSITY OF OXFORD OXFORD OX2 6GG, UK su: Differentiable functions Definability theory (Mathematical logic) Model theory Recursive functions Algorithmic randomness Applied mathematics Algebraic logic sug: subj: Differentiable functions Definability theory (Mathematical logic) Model theory Recursive functions Algorithmic randomness Applied mathematics Algebraic logic keyword: 03C10 03C60 12H05 12H20 13N15 abstract differential equation definable derivation differentially closed field model theoretic algebra reduct ab: Let ${\cal F}$ =(F; +, .,0, 1, D) be a differentially closed field. We consider the question of definability of the derivation D in reducts of ${\cal F}$ of the form ${\cal F}$R = (F; +, .,0, 1, P)P ε R where R is some collection of definable sets in ${\cal F}$. We give examples and nonexamples and establish some criteria for definability of D. Finally, using the tools developed in the article, we prove that under the assumption of inductiveness of Th (${\cal F}$R) model completeness is a necessary condition for definability of D. This can be seen as part of a broader project where one is interested in finding Ax-Schanuel type inequalities (or predimension inequalities) for differential equations. 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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