The removal of $\pi $ from some undecidable problems involving elementary functions

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. ABSTRACT. We show that in the ring generated by the integers and the func-tions x, sin xa and sin(x sin Xn) (n = 1, 2,.. .) defined on R it is undecidable