Elementary differences between the (2p)-c. e. and the (2p+1)-c. e. enumeration degrees

Abstract

It is proved that the (2$p$)-c. e. e-degrees are not elementarily equivalent to the (2$p$+1)-c. e. e-degrees for each nonzero $p \in \omega$. It follows that $m$-c. e. e-degrees are not elementarily equivalent to the n-c. e. e-degrees if $1 < m < n$.