Alfred Leon Foster (1904-1994) was an American mathematician.Alfred L. Foster, U. of California: In Memoriam, 1995
/ref> He was a professor at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

from 1934 until 1971. In 1932 he was an Invited Speaker at the ICM in Zürich. In 1934 he accepted a regular position at

Berkeley Berkeley most often refers to: *Berkeley, California, a city in the United States **University of California, Berkeley, a public university in Berkeley, California * George Berkeley (1685–1753), Anglo-Irish philosopher Berkeley may also refer ...

. At that time Griffith Evans was Head of the Mathematics Department and was charged by President Sproul with building a first-class mathematics center, which he did. Alfred Foster and Charles Morrey (who became the first department chairman after Evans' retirement) were Evans' first two appointments. Except for subsequent sabbatical leaves, spent most notably in

Freiburg Freiburg im Breisgau (; abbreviated as Freiburg i. Br. or Freiburg i. B.; Low Alemannic: ''Friburg im Brisgau''), commonly referred to as Freiburg, is an independent city in Baden-Württemberg, Germany. With a population of about 230,000 (as o ...

and

Tübingen Tübingen (, , Swabian: ''Dibenga'') is a traditional university city in central Baden-Württemberg, Germany. It is situated south of the state capital, Stuttgart, and developed on both sides of the Neckar and Ammer rivers. about one in three ...

, Foster served continuously at Berkeley until his retirement at the then-mandatory age of 67 in 1971. Foster's Ph.D. dissertation and his first few papers were in the area of

mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...

. Starting from this point, he soon focused his interest on the related theory of Boolean algebras and Boolean rings, and was thus led from logic to algebra. He extensively studied the role of duality in Boolean theory and subsequently developed a theory of n-ality for certain rings which played for n-valued logics the role of Boolean rings vis-a-vis Boolean algebras. 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. Foster was married to Else Wagner; their marriage produced four children and eight grandchildren.

Selected publications

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References

20th-century American mathematicians University of California, Berkeley College of Letters and Science faculty Princeton University alumni 1904 births 1994 deaths California Institute of Technology alumni {{Mathematician-stub