Constructing $\ddot{I}‰$-free Hardy fields

Abstract

We show that every Hardy field extends to an $\ddot{I}‰$-free Hardy field. This result relates to classical oscillation criteria for second-order homogeneous linear differential equations. It is essential in [10], and here we apply it to answer questions of Boshernitzan, and to generalize a theorem of his.

51 pp.; revised following remarks by a referee; to appear in J. Analyse Math