The Peterson reaction is stereospecific. This is because it is an E2-elimination proceeding via an anti-periplanar transition state. In principle, it can therefore be used to make single geometrical isomers of alkenes, with the geometry depending on the relative stereochemistry of the starting material.
CLICK the two different diastereoisomers below to see which alkene is formed under acidic conditions:
There is another version of the Peterson reaction which uses base (such as potassium hydride) to promote elimination. Click base-promoted Peterson reaction to see how diastereoisomer 1 behaves under basic conditions.
I. Fleming, A. Barbero and D. Walter, Chem. Rev., 1997, 97, 2063–2192.