Except for subsequent sabbatical leaves, spent most notably in Freiburg and Tübingen, Foster served continuously at Berkeley until his retirement at the then-mandatory age of 67 in 1971.

He extensively studied the role of duality in Boolean theory.

The late Benjamin Bernstein of the Berkeley mathematics faculty was his collaborator in some of this research.

This work culminated in his seminal paper "The Theory of Boolean-like Rings", appearing in 1946.

[1] Foster was married to Else Wagner;[3] their marriage produced four children and eight grandchildren.