\input zb-basic
\input zb-ioport
\iteman{io-port 01236714}
\itemau{Ahmad, Seema; Lachlan, Alistair H.}
\itemti{Some special pairs of $\Sigma_2$ e-degrees.}
\itemso{Math. Log. Q. 44, No.4, 431-449 (1998).}
\itemab
An e-degree ${\bold a}$ is called low if every set in ${\bold a}$ is $\Delta_2$. In this paper it is proved that: There exists a non-zero low non-splitting e-degree (Theorem 2.1). For every non-zero low e-degree ${\bold a}$ there exists a $\Sigma_2$ e-degree ${\bold b}$ such that ${\bold a}\perp {\bold b}$ and for every e-degree ${\bold z}$, if ${\bold z}<{\bold a}$ and ${\bold z}\nless{\bold b}$, then there exists ${\bold y}$ such that ${\bold y} < {\bold b}$ and ${\bold y}\cup{\bold z}={\bold a}$ (Theorem 3.1). From this results follows that there exist $\Sigma_2$ e-degrees ${\bold a},{\bold b}$ such that ${\bold a}\perp {\bold b}$ and every e-degree strictly below ${\bold a}$ is also below ${\bold b}$.
\itemrv{R.Sh.Omanadze (Tbilisi)}
\itemcc{}
\itemut{enumeration degrees; Turing degrees; low degrees}
\itemli{doi:10.1002/malq.19980440402}
\end