EFFECTIVE DEFINABILITY OF KOLCHIN POLYNOMIALS

doi:10.1090/proc/14869

	EFFECTIVE DEFINABILITY OF KOLCHIN POLYNOMIALS
	Freitag, James 2; Sanchez, Omar Leon 3; Li, Wei 1
刊名	PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
	2020-04-01
卷号	148 期号:4 页码:1455-1466
关键词	Differential fields Kolchin polynomial effective definability in families
ISSN号	0002-9939
DOI	10.1090/proc/14869
英文摘要	While the natural model-theoretic ranks available in differentially closed fields (of characteristic zero), namely Lascar and Morley rank, are known not to be definable in families of differential varieties; in this note we show that the differential-algebraic rank given by the Kolchin polynomial is in fact definable. As a byproduct, we are able to prove that the property of being weakly irreducible for a differential variety is also definable in families. The question of full irreducibility remains open; it is known to be equivalent to the generalized Ritt problem.
资助项目	NSF[1700095] ; NSFC[11688101] ; NSFC[11301519] ; NSFC[11671014]
WOS研究方向	Mathematics
语种	英语
出版者	AMER MATHEMATICAL SOC
WOS记录号	WOS:000518176000009
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/50873]
专题	中国科学院数学与系统科学研究院
通讯作者	Freitag, James
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, 55 Zhongguancun East Rd, Beijing 100190, Peoples R China 2.Univ Illinois, Dept Math Stat & Comp Sci, 851 South Morgan St, Chicago, IL 60607 USA 3.Univ Manchester, Sch Math, Oxford Rd, Manchester M13 9PL, Lancs, England
推荐引用方式 GB/T 7714	Freitag, James,Sanchez, Omar Leon,Li, Wei. EFFECTIVE DEFINABILITY OF KOLCHIN POLYNOMIALS[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY,2020,148(4):1455-1466.
APA	Freitag, James,Sanchez, Omar Leon,&Li, Wei.(2020).EFFECTIVE DEFINABILITY OF KOLCHIN POLYNOMIALS.PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY,148(4),1455-1466.
MLA	Freitag, James,et al."EFFECTIVE DEFINABILITY OF KOLCHIN POLYNOMIALS".PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 148.4(2020):1455-1466.