Is it known if $0^{(\omega)}$ a minimal cover in the arithmetic degrees? In the Turing degrees to show that $0'$ (indeed $0^{(n)}$) isn't a minimal cover one uses the density of r.e. degrees. However, given that it's not known if downward density holds for the REA sets (even in the arithmetic degrees) is it known if $0^{(\omega)}$ a minimal cover in the arithmetic degrees?

EDIT: To be clear, I'm asking whether it's the case that there is an arithmetic degree $X$ such that $X <_a 0^{\omega}$ but that there is no $Y$ with $X <_a Y <_a 0^{\omega}$ where $<_a$ is the relation "is arithmetic in"