Fraenkel, Abraham Adolf (1891–1965)

German-born Israeli mathematician. He wrote many textbooks on set theory, and also investigated the axiomatic foundations (see axiom) of mathematical theories

Fraenkel became very involved with set theory as it had been formulated in 1908, in the axiomatic system put forward by German mathematician Ernst Zermelo. He proposed in 1922 a solution for Zermelo's unexplained notion of a ‘definite property’, though his explanation did not become accepted.

His research led him to posit an eighth axiom (to follow Zermelo's seventh), an axiom of replacement, which stated that if the domain of a single-valued function is a set, its counterdomain is also a set. Fraenkel's works include Einleitung in die Mengenlehre (1919), Abstract Set Theory (1953), and Foundations of Set Theory (1958).

Fraenkel, born in Munich, studied there and at Marburg, Berlin, and Breslau (now Wrocław, Poland). He was professor at Marburg 1922–28. In 1929 he emigrated to Israel and taught until 1959 at the Hebrew University of Jerusalem.