Fraenkel

Fraenkel is a surname of German and Ashkenazi Jewish origin. It is associated with several scholars in mathematics and logic, and it is particularly linked to foundational theories in set theory through the work of Abraham Fraenkel.

In mathematics and logic, Fraenkel most notably refers to Abraham Fraenkel (1891–1965), a German-born logician who helped develop the axiomatic approach to set theory. Fraenkel, Zermelo, and others contributed to the formulation that would become Zermelo-Fraenkel set theory. Fraenkel is especially remembered for introducing the axiom of replacement, a principle stating that the image of a set under any definable function is again a set. The resulting framework is commonly called Zermelo-Fraenkel set theory, and when combined with the axiom of choice it is known as ZFC—the standard foundation for much of modern mathematics.

A related construction bearing Fraenkel’s name is the Fraenkel–Mostowski model (FM model), a method used in set theory to build models with atoms (urelements) to investigate independence results, including implications for the axiom of choice. This technique has played a significant role in the study of how various set-theoretic axioms relate to each other.

Beyond these mathematical contributions, the surname Fraenkel appears in historical and biographical contexts, attached to scholars and professionals across fields. In encyclopedia and reference writing, Fraenkel may be encountered as a surname associated with such figures or, more broadly, as part of discussions of foundational set theory.