Definition:Theory of Types

Definition

The theory of types is a system of axiomatic set theory which is originated by appending a further axiom to the Axiom of Abstraction stating:

A set cannot be an element of itself.

Also see

• Axiom:Axiom of Foundation

• Definition:Class Theory

Historical Note

The theory of types was devised by Bertrand Russell in $1910$ as an attempt to resolve what is now referred to as Russell's Paradox.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): type
• 1993: Richard J. Trudeau: Introduction to Graph Theory ... (previous) ... (next): $2$. Graphs: Paradox