The removal of <IMG > from some undecidable problems involving elementary functions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

The removal of from some undecidable problems involving elementary functions

Authors:	M Laczkovich

Institution:	Department of Analysis, Eötvös Loránd University, Budapest, Pázmány Péter sétány 1/C 1117, Hungary

Abstract:	We show that in the ring generated by the integers and the functions $x, \sin x^{n}$ and $\sin(x\cdot \sin x^{n})$ $(n=1,2,\ldots )$ defined on $\mathbf{R}$ it is undecidable whether or not a function has a positive value or has a root. We also prove that the existential theory of the exponential field $\mathbf{C}$ is undecidable.

Keywords:	Undecidable problems rings of elementary functions

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文